Thanks guys for the feedback.
I mustered up the courage to say "thanks, but no thanks" to that professor, and he was very understanding about it.
Problem is, the same thing happened with two other PIs whom I met during recruitment week and discussed the possibility of rotations. When I asked then if they had availability/funding for someone like me, their response was "well, I can't really be sure right now but maybe". Now, it seems to be a flat out no.
I don't know if this is somehow related to the timing that PIs find out about funding, but to me it kinda seems deceiving. Like, I was hoping there would be a chance to work with them and thats why I accepted this school. It seems as if all of the labs I wanted to join are full/have no prospective of funding... Should thesis lab hunting be a numbers game? Perhaps I chose the wrong school?