To be honest, the winners didn't really saw their actions as the fall of Rome. People didn't woke up the day after the fall of Rome thinking "damn, Rome fell, now what will be of us". They were pretty "meh, a guy deposed the previous guy, and instead of calling himself emperor, putted himself under the official rule and protection of the Roman Empire, now seated in Constantinople". It was a much less traumatic event than people realize. The same way using "invasion" is also a pretty exaggerated vision of what we nowadays think happened.
I am with you on that one. Winners usually write the history of the wars and, in many cases, the history of the defeated peoples. Take men like Viriato, Boudica or Arminius, their portrayal is clearly based on Greco-Roman philosophies, Greco-Roman ideas, Greco-Roman history, etc. They are the brave barbarians, still pure and uncorrupted by wealth, being the total opposite of the Romans that fought them.
And they are also a pretty good example of how winners writing history isn't the same as winners writing history where they are the heroes, difference that seems to be ignored in this discussion. And besides, we can't truly apply that concept as literal, much less to the modern period. And, I think, the idea that winners can write history AND present themselves in a relatively unsympathetic light, also helps to explain why the Fall of Rome is seen as profoundly negative (which it was, as a classicist that is obviously my stance and interpretation), to which also helps the fact that the Romans had the last laugh: their customs, language, laws, some organizations, etc. did end up prevailing, in some part, against the "winners".
We can win and see ourselves as the villains, why should the people writing their history be any different?