Dear saguaros,
Thanks for the offer. Unfortunately, as a basic rule, I do not share admin passwords. There can be sensitive information inside even the most basic website, and my customers would be pretty upset. I would advise to stop this method in this support page too, but I guess that is non of my business, and I understand that it is convenient.
On the other hand, I managed to track down the problem, and it is not a 3rd party plugin, and not even something inside Joomla. My htaccess file contained a security improving part to force index.php parsing before index.html. Removing this clearly solve the problem. Now I am trying to fabricate an exception for the involved T4 library page (to be able to turn on the rule again), any advice is welcome.
Best