Most of my ASMs are actually non-equity interns, apprentices, or people with day jobs, doing theater on the side, so I'm generally pretty hands-on until I'm sure they can handle things. I always have them give me copies of their paperwork, so I can make sure it’s accurate, functional, and understandable to someoen other than it’s creator (as well as just in my possession should they be hit by a bus).
As others have mentioned, I’m usually more involved early in rehearsals. As we get closer to tech, ideally the ASM will take ownership of the set and props, and have the initiative to do as much as possible on their own. But in many situations, I do help. Often it’s because there is more to the shift than one person can efficiently do on their own, and we know we will have crew (or technology) to help the ASM during the run, so I’ll help in rehearsals knowing we’ll have other resources later. Sometimes we are in the middle of intensive actor stuff, and want to move into the next piece of work quickly, so I’ll help speed up the shift rather than sit on ceremony while the ASM does the shift in real time. Other times we are planning to make the shift highly choreographed in time for the run, but aren’t ready to work out the mechanics of that yet, so I’ll jump into the shift in the interest of keeping the rehearsal moving forward.
I agree with Scott’s point about breaks; I usually tell my ASM ahead of time that the AEA break is the only one I get (pee now or forever hold your pee!), but I’ll give them a staggered break later if they work through theirs. Still, I usually return to the rehearsal space bfore the break is over to be sure we’ll be ready to get back to work.
It sounds like you and your ASM responded professionally to truly unhelpful actor input. Maybe his comment comes from working on shows where more crew was expected for tech, and that’s why he’d see the SM working on shifts in rehearsal. Or, he’s worked on shows where the ASMs were incompetent, and the SMs had to jump in or nothing would get done!