In the grand tradition of digressing from the OP, lets continue this post.
I did a bit of research to see if opinion had moved on from when I did copper work (and plumbing).
My research absolutely agrees with the part of your statement in italics.
Crystals form in copper as it is worked.
Heating to red heat randomizes the structure, breaking down the crystals. Fast quenching 'freezes' this state, just as you've said above.
Absolutely pure copper might behave differently, but the 'copper' that we have access to certainly requires annealing with a fast quench. Slow cooling after heating isn't as effective.