Caretoguess: well, it's not the only thing missed in FE10. Data transfer glitch, inconsistencies with Terin/Turin, Muarim's profile issue...
Heather can become a whisperer. Besides, if she couldn't class change
why was she gaining EXP at level 20?

Could you still gain EXP after the glitch? Theoretically, you could just keep looping her level, right?... Hmm...
Yes, I could. (The way it went: [lv/exp] 20/~95 -steal- 20/0 [no level or class up] -steal- 20/10 ...) I didn't go beyond 20/30 or 40, so I don't know of it could have kept looping. However, next chapter I went to the base to try and upgrade her class with BEXP, and it
did work.