I do get what you are saying, it's just that there's something weird going on as it really should simply work. I literally just tried it to be sure.
I recorded a slow melody while my project was running at 132 BPM. After recording, the clip parameters show:
Then, I disable warping:
Finding the tempo for the whole project based on that clip; with the metronome on and adjusting the project tempo while listening. Happened to land on 100 BPM, heh:
Then I enable warping on the clip again. Live asks this:
Answer yes, as the whole point is to keep the timing as it is, and be able to adjust it further with warping enabled.
As a result:
The clip is still sounding as it was when I recorded it, and warp is enabled again, clip tempo matching that of the project.
Also note that you can of course in turn adjust the Seg. BPM of the clip manually if there's a discrepancy in that sense. You don't need to rerecord in order to get a fresh "original" tempo assigned for the clip.