I was constantly monitoring the voltage with a DMM. When the pro mini is powered via the USBasp dongle it is constantly at 3.4 V +/- 0.1.
Anyway, even powering arduino via a stabilized power supply at 3.3V does not affect the defect.
Now I have two brand new pro mini in front of me. Nevertheless, I would be sure of what I'm doing before going to fry them too. 
BTW, after the setting of the four fuse bits, I clearly remember a line reporting a "content mismatch error" against a file called "empty.hex".
If I remember right, the following line was reporting an error like "0x00 is not 0x0c", or something like that.
Unfortunately, when I clicked on the command "Upload" the previous output on the screen was wiped out. Was better to make a copy of that text-output before going further. Shame on me!