Oh actually, I used a fat ps2 as well (with manually installed fliptop), although I can imagine that something similar can happen to the slimline. And yeah, it was pretty annoying how there was something wrong with the way this thing was manufactured.
In case you're really curious as to how my problem is visualized, think about that coiled wire that's wrapped around the hinge of the fliptop. After the coil, the wire sticks out and was actually long enough to touch the disc
.