Nail on the head, Duncan.
I recently recorded an album in a studio, mostly because the engineer is a close friend and I had always wanted to record with him previously when in black metal bands but the other members never went for it. I said 'fuck it, I'll record my noise with him' and it turned out great because I went in with no expectations.
I improvised a load of noise using great gear I would otherwise have no access to (Korg MS-20, huge Ampeg bass cab, the engineer's entire pedalboard, incredible room and vocal mics) and expertise I haven't grasped yet myself (recording set-up plus Pro-Tools fluency).
The engineer then edited it down to the bits that most grabbed him and essentially did all the producing. The result was a pretty varied album with elements I would never have considered bringing in on my own, as well as the engineer's preconceptions about noise (he's not a fan) being challenged.
I would 100% call it a collaboration with the engineer rather than the engineer simply recording something as straightforward as I would record at home.
You can hear a track of it here, it's going to be released on Phage Tapes soon-
https://www.youtube.com/watch?v=vYy1LnSnRTw&t=66s