There is a check at the beginning if that folder is writable. Maybe there are still conflicts with restricted rights, e.g. the server not being able to create files?!
Good call, the check indeed said everything was fine, but like you said there was still a problem with the permissions. I think what solved this problem was ultimately giving the Network Service write permissions to the folder.
Unfortunately, while I now completed the installation, it's now crashing with an IIS 7.0 error on the admin page:
HTTP Error 500.0 - CDbException
The page cannot be displayed because an internal server error has occurred.