I am not doubting your explanation, but why would Fox care if they were called mutants or not?
Fox would rather that Marvel didn't use quicksilver or the scarlet witch, especially considering how they're pretty important because they're Magneto's kids. They'd rather have the characters for themselves. If Marvel called them mutants, then Fox would have a pretty credible claim on a breach of contract. Marvel refraining from calling them mutants makes the ownership over the characters murky, which means starting costly litigation doesn't really make sense.
I'm not even sure that it's a compromise. I think it's just a gray area, and Marvel isn't calling them "mutants" to keep Fox from suing them for breach of contract.