OK it's getting weirder:
You know how ISPconfig creates symlinks like webX -> www.domain.tld
Now I just saw that the relevant symlink is not a symlink but an actual folder with the name of the domain of user/website webX. There is a huge Apache log file in there, but no log files in webX/log
Also when I go into ISPconfig, open the relevant site, and click the statistics tab: The statistics are all at 0.