Take something like Dark Phoenix, who starts out at a cheap point cost but can heal above her starting line.

Assume she heals significantly above her original line but is then KOed.

Does the opponent score her at just her original points cost, or does the healing to a higher value affect that?

It does not usually affect scoring. No one would have played Dark Phoenix if her healing once would have bumped her to 300 points.

Ok. Are there any obvious cases where such would?

Unless otherwise stated (like with replacement characters) your number of points scored is the character cost (so the character point value plus any additional cost like optional traits)

21.12b Scoring Replacement Characters
When one or more characters replace a character, and all of that character’s replacement characters are KO’d, score victory points equal to the point value of the replaced character or the total point value of the KO’d replacement character(s), whichever is greater.

Coyote's own hit the big, and I think the only modern legal one. This isn't healing, but it does change the cost of the character (and explicitly tells you so):



It was also an issue with characters going on a solo adventure from team bases pre-errata, but that hole is long closed.