How about /home/bla/public_html/blabla and /home/bla/public_html? Also, group membership does not mean that the user will have proper permissions. See also if there are ACL entries and what the group permissions are on each of the directories.

Are CGI scripts running with suEXEC permissions to a different user?

It might help to diagnose this if you were to show us what the process entry looks like for the script that is misbehaving, what the directory entries between /home/blah and /home/blah/public_html/blabla look like, and anything else that may be pertinent. With what you have provided, the best we can do is like throwing darts at a target while being blindfolded.