Billing for random things outside of the agreed upon scope of work is actually unreasonable. It’s something covered in every contracting agreement I’ve ever been a part of.
Maybe they could point to some contract that maybe would have covered it, but when your contractors start billing you for sending quick emails about unrelated things you didn’t ask them to look into, it’s not a good sign. When contractors bill for quick emails they don’t bill for the 3.7 minutes it took to write, they round up to some bigger number like an hour.
Anecdotally, every time I’ve encountered contractors who started billing per individual communication that they initiated (not something requested) or started finding new things to bill us for that we didn’t ask, it was a sign that we were a target being milked for billable hours. Some contractors have a lightbulb moment when they think nobody is scrutinizing their billing and think they discovered an almost infinite money glitch by initiating new things that they can bill for. None of the good contractors I’ve worked with over the years would even think to bill for an individual short email.