Yes, in that case, if the new name/directory seems closer to the "wrong" file, the history will be taken from the wrong file.
Then again, this is a very theoretical case, I've never seen this happen in practice; besides, if files end up being identical but with differing history, then in most cases, their history is related. It's rather unlikely that history is unrelated, but files end up identical.
Wouldn't this be common for files like .cvsignore or similar files that contains a small set of rules that may exist in many instances throughout the source code?