We already know what the source that they refer to is, it was in Neo's conversation with the Oracle in Reloaded:
Oracle:...and when it does a program can choose to hide here or return to the source.
Neo: The machine mainframe.
Oracle: Yes. Where you must go. Where the path of The One ends.
So, the source would be the root level of the central machine computer system. So the room itself could not be the source - in this sense at least. But it is stated (as Omega informed me) that in ENTER THE MATRIX the Oracle says that Neo's mind touched the source and this is the reason for his coma. Also, the architect says that he is the one who designed the matrix, so he is the source of the programming for that world - which Neo does interact with. (see my posts in the Best evidence thread if you haven't already)
Jedi is right. The prophecy is definitely false. The quote from the movie helps Neo realize this when he realizes that she is the Matrix's "Mother." She and the Keymaker never actually say that they are helping the resistance, but rather that "we are all here to do what we are all here to do." Which is to layout the path for "the One" to follow in order to promote the continuation of the matrix.
So is the architect the source? Of the programming writes, yes, but not the root access that was refereed to. Neither is his room for that matter, I think that has to be a construct outside of the matrix program itself. (again see my posts in Best evidence if you aren't familiar with this argument. 😛)