In an attempt to find out whether I could make a func_door_rotating rotate on a tilted axis instead of "only" X, Y or Z, I found out this weird behaviour.
There are three doors in this map, all of them have their default rotating axis (a.k.a. "Z"). The first door is the "control subject", with all values left as default. The second and third doors have 30 degrees set on Pitch/Yaw/Roll - one of them in X, the other one in Y.
Setting Pitch/Yaw/Roll makes them appear in game in a different position than the brushes were placed in Hammer, but the rotating axis remains absolute (X, Y or Z) instead of sticking to the rotated door. The weird thing is that the doors behave differently depending on which side they are approached from: Going one way they rotate normally, going the other way they rotate... in a weird way.
The semitransparent green sticks next to the doors are just func_illusionaries to illustrate the axes the doors are intended to rotate on.
It appears it's not possible to make a door rotate on a tilted axis like I wanted. I suppose whoever wants to do that will have to make a model door, with opening animations in whichever axis they want.
I don't know whether anyone will consider this useful insight or just map spam, but since I've seen some weird hacks with entities to pull off cool stunts, I can hope that someday, someone will find a use for this.
I also hope that in a vague future, a new version of TWHL will give its errors without trashing everything you've typed, making you type all your map description again because you clicked the .bmp screenshot instead of the .jpg.