It is clear the US military in Iraq is a far cry from a liberating army. The US propaganda machine packed the "freeing" of Iraqis from a ruthless tyrant into its extensive collection of rationales for invading Iraq, but that was not a line they expected anyone to actually swallow. At most it was thrown out there so it could be taken up as the publicly stated excuse for support of the war by the more squeamish types who need a humanitarian spin to justify getting behind carnage of war to their progressive friends.
In reality nearly everyone on either side of the divide understood the war was actually about power, empire, Israel, oil, attacks on WTC, unfinished business, "islamofascism" and blowing shit up. A far greater number of people got behind the invasion due to erroneous and ridiculous belief - carefully nurtured albeit never expressed clearly by the propaganda machine - that Iraq had something to do with the attacks on WTC in 2001 than was the number of people who got behind it because they expected the invaders to be greeted with flowers and kisses.
Additionally the last people who imagined the invasion force is going to be an army of liberation were the soldiers that were going to make it up. Not only did they not presume they would play the role of liberators, but they would not want to in the first place. They had not signed up to be shipped half way across the world to liberate Muslim foreigners, they had signed up to blow away America's enemies. Therein lied one of the most basic problems for the prospect of the US military as a liberating force in Iraq. The troops did not want to be liberators. They did not want to be heroes of Iraq, they wanted to be heroes of America. Understandably they did not care for the Mesopotamia Arabs enough to want to be shot at for their benefit.
The helm understood this all too well and anyway privately felt the same. It also understood it it is far easier to dispatch troops with an unspoken agreement that they would not actually have to behave as altruistic liberators and put lives of liberated Iraqis before their own safety. So instead they would be given every conceivable leeway and room to use deadly force whenever they perceived themselves to be in any amount of danger, regardless of what hazards that brought upon ordinary Iraqis for whose benefit they were supposedly there.
Therefore regardless of Saddam Hussein being an unpopular dictator and the US invasion resulting in his removal the US military could never be labeled a liberating force. But can foreigners in theory be liberators and be seen as liberators?
In some cases the answer would have to be yes. In the instance of the Philhelenes for example. During the Greek Revolution of 1821, hundreds of Germans, Frenchmen, Italians and Britons came to the aid of the Greeks in their struggle to overthrow the Ottoman Empire and continue to be revered by them for their contribution. But the Philhelenes being private citizens were in much different position from an eventual interfering foreign army.
Firstly, being volunteers they had proved just by coming that they care about Greeks sufficiently to risk life and limb for them thus they would have never contemplated putting their own safety before the lives of the populace and were not going to be the cause of any "collateral damage". Also being there of their own accord they were free to leave had they discovered that actually they were not welcome. Lastly they were not a part of a bureaucracy controlled by a government abroad, they were not agents of a foreign government. Instead they joined with Greek formations and subordinated themselves to Greek commanders. They were not interested in imposing nor could they thus impose on the Greeks their own vision of how Greece should be organised after the war. They subordinated their fighting wholly to whatever the Greek agenda for when freedom comes.
On the contrary it is exceedingly hard to find examples where a military of a foreign government rather than private individuals were welcomed as liberators. Certainly no case can be found of the populace showing gratitude to a foreign military for deposing a local home grown government and then establishing a client regime in its place. Even where the home grown government was deeply criminal and unpopular there is a fundamental contradiction that in this respect makes regime change a failing proposition from the start. A government can not be seen legitimate as long as it owes its existence to foreigners, and a government seen as illegitimate requires some form of occupation to maintain.
Crimes of the previous, homegrown regime could not result in the subsequent foreign installed government enjoying any amount of legitimacy even in Cambodia, where the preceding rule was by the murderous Khmer Rouge who were deposed in 1979 in a war they had started with Vietnam. The guerrilla resistance to the Vietnamese was always overstated, on the ground it consisted of a few ten thousand Khmer Rogue remnants animated by aid from the United States and China with the former playboy king Norodom Sihanouk representing their public relations front. The tired nation had no taste for another war. However the Cambodians who were more than glad to see the backs of the Khmer Rouge did not in the least appreciate the imported government of the opportunistic Heng Samrin which was therefore unable to create any meaningful power autonomous from Vietnam. A situation that did not change until 1989 when the Vietnamese left and largely left the government they had installed to its own devices
The only real examples of foreign militaries being seen as liberating forces are when they expel a different set of foreigners, provided the other foreigners were even worse and that the new foreigners do not overstay their welcome. This indeed seems to be the decisive factor in judging whether a foreign military will be seen as a liberating force. Anglo-Americans invading France in 1944 despite clearly not being primarily concerned about the wellbeing of the French populace, as thousands of civilian deaths in France due to allied bombing can attest to, were except in places directly affected by the carnage of allied ordnance welcomed as liberators of sorts for driving away the Germans who had dismantled the independent French state.
Not interfering with a home grown government arising uninterrupted and uninfluenced as important factor as it is however does not always seem to be a prerequisite to be seen as liberators if the evicted foreigners had been sufficiently unpopular and if the new status grants the people in question significantly more independence than they could enjoy before. Eg the Soviets are still honoured for liberating Czechoslovakia from the Germans in 1945 even after they had influenced Czechoslovak politics to transform Czechoslovakia into a communist state and even if their later presence was resented. Similarly the Russians are still revered for freeing Bulgaria from the Turks in 1878 despite the tsar's meddling in the aftermath of the war meant independent Bulgaria would be a conservative monarchy and not a republic as were the aspirations of Bulgarians.
Finally we should mention cases where foreign armies expelled a different set of foreigners and moved in at their expense bringing new foreign authority without being seen either as liberators or occupiers but instead being met with ambivalence. Such cases however while numerous in number are confined to pre-modern societies. Societies before mass literacy, mass media and mass politics. Confined to time and place where the populace is not permeated with democratic spirit and does not see itself as the entity upon which it rests the ability to grant a government its stamp of approval and legitimise it, but instead being unable to conceive of such thing as government from the people perceives all government and potential government as essentially alien and - having no expectations of freedom from government - inevitable. For example the French taking over the Austria`s Adriatic coast in 1809 which found the populace indifferent, seeing French rule and Habsburg rule as interchangeable and equivalent.