This might be related to the installed/used version of curl and GitHub’s switch to https.
By default I think curl will error at all certificates if not given a ca bundle (or a switch to override the error).
Ok, found the problem.
A more recent version of curl installed with MAMP was earlier in TM's PATH than in my .bash_profile's PATH.
Maybe you could add a which curl in the "Check Requirements", Hans. ;)
Thank you both for your answers.