While I don't expect an exec to be at the same level as current researchers, they should know something about the field.
Her music degree is not completely relevant, tho it is concerning. The rest of her resume (and total lack of relevant experience) is more damning.
Look, I personally know someone who's a C level in a tech company, with a political science degree. But his resume shows 15 years of full-time employment in his current field, plus summer jobs in university, and going back to high school. So with 20 years of experience in the field, his degree doesn't matter so much.
Your counter position seems to say that execs can manage a division while knowing nothing about what the division does. There's just no way that's true. The exec must know something in order to be able to prioritize projects, set goals, mediate disagreements, etc.
Or would you say that someone who has no education in a field, and no experience in a field, is qualified to be an executive-level manager for that field?
That's just hard to believe.