I do think that Dumbledore was the one that gave him the cloak.
However, McGonagall was shocked that he had -an- Invisibility Cloak, not -the- Invisibility Cloak. If she knew that Dumbledore had the Potter's cloak (assuming same as canon), then the odds of Harry getting a completely different cloak would be low enough that she could assume that Dumbledore gave Harry part of his inheritance.
I think that she just made an assumption, considering it very unlikely that he got it any other way since his access to the family vault is limited.
Update: Discussion has moved on to a new thread.
After 61 chapters of Harry Potter and the Methods of Rationality and 5 discussion threads with over 500 comments each, HPMOR discussion has graduated from the main page and moved into the Less Wrong discussion section (which seems like a more appropriate location). You can post all of your insights, speculation, and, well, discussion about Eliezer Yudkowsky's Harry Potter fanfic here.
Previous threads are available under the harry_potter tag on the main page (or: one, two, three, four, five); this and future threads will be found under the discussion section tag (since there is a separate tag system for the discussion section). See also the author page for (almost) all things HPMOR, and AdeleneDawner's Author's Notes archive for one thing that the author page is missing.
As a reminder, it's useful to indicate at the start of your comment which chapter you are commenting on. Time passes but your comment stays the same.
Spoiler Warning: this thread is full of spoilers. With few exceptions, spoilers for MOR and canon are fair game to post, without warning or rot13. More specifically: