Just a shot in the blue: To isolate the grounds of your sig gen and scope... you didn't happen to use a multi-outlet extension cord, isolated the ground of that, and plugged both devices into the same extension? That would make both devices basically isolated from mains earth/ground, but the grounds of the scope would still be connected to the ground of the signal generator.
Well, that's embarrassing. It turns out you were guessing right! I didn't think of the "multi-socket shorting independent of house earth". But I could have sworn I tried all possible combinations (isolating the scope plug, isolating the signal gen plug, isolating the plug of the multi-outlet extension cord / multi-outlet power strip), so it should have worked anyways.
Maybe I had the right isolation (by "chance"), but the signal didn't look clean enough for some other reason and that threw me off course...
But it's good I made the mistake to be aware of my misconception about the multi-outlet power strip.
Thanks! Better knowing why you are a fool than staying wrong while clueless haha (sorry about the professor).
I was a bit nervous about testing the power plugs with the multi-meter, but I suppose I could have done continuity testing between the scope bnc and signal generator bnc plugs (the outer shells), safely.
Doing that indeed confirmed the (now obvious) direct connection between the earth plugs in the multi-outlet power strip (and therefore the scope and signal gen). I somehow assumed that the connection would just be made in the house wiring, later (and therefore not occur if the main's earth is not connected). But since the multi-outlet strip gets connected to the wall outlet by a single power plug, it should have been obvious that this could not be the case (and all individual sockets earth must be joined together). Oops.
I'll post a "success scope" image and a summary of the essential points, in case someone else stumbles upon this again.
Thanks again everyone for your patience.