AWS doesn't consider them sensitive, but some organizations do. My feeling is that I would rather avoid leaking any info about my AWS environments. Just because AWS doesn't think they can be dangerous doesn't mean someone else won't find a way.
I did this at a previous employer. I leveraged a Lambda functions and tags applied to instances to determine when they should be and when they should be off.
It's odd that regular testing wasn't part of a compliance framework for them. BC/DR testing has been part of every security/compliance framework I've worked with.