Sorry, but git logs prove nothing. Git allows rebase and modification of commits. Even a full log of when pushes to github happened prove nothing - I can work during the day and just commit later.
It's a little unclear what you mean by "modify", so just to be clear here: you can't alter an existing commit.
You can certainly fake any timestamp you want to start with, or you can create a new set of commits with a different timestamp (which is what rebase does), but you can't change an existing commit - the hash would be wrong.
>but you can't change an existing commit - the hash would be wrong.
True - however as long as nobody ever saw that commit, nobody will know. So the only way a git log could ever constitute a proof would be that you immediately push to a tamper-proof audit system right after your commit.