OK, so all the blah blah blah in owncloud page about the convenience of using the installer is simply propaganda. If I had known it, I had used my own "download script from web and install it" php script.
BTW I have solved the issue re-installing 8.0.1 (I wonder why I can't install 8.1.x now). I will try to overwrite it with 9.x.
I also compare the htaccess file made by 8.0.1 with the one made by 9.x, just in case that is what causes the problem.
8.0.1 lacked the following lines:
# Add security and privacy related headers
Header set X-Content-Type-Options "nosniff"
Header set X-XSS-Protection "1; mode=block"
Header set X-Robots-Tag "none"
Header set X-Frame-Options "SAMEORIGIN"
Header set X-Download-Options "noopen"
Header set X-Permitted-Cross-Domain-Policies "none"
SetEnv modHeadersAvailable true
Maybe these were the ones disallowing me from installing owncloud inside a sub domain in a shared host. But I swear I tried deleting the whole .htaccess before posting here.
PS -- having a history list of owncloud releases on the webpage would be useful for those, as me, having to roll back to very old releases and updating them before. I had had to made a php script to detect all releases between 8.0.1 and 9.1 and update my install (8.0.1 did not allow for auto updates).