Rigid? Maybe. And in fairness, I don't do a lot of rehearsals, and neither do most of the guys I play with, all solid, reliable, top-tier guys who stay pretty busy because they do their homework at home. When we do have a rehearsal, there's flexibility if someone has to bail in favor of a paying gig, but that almost always happens with advanced notice.
As far as making mistakes or forgetting things goes, it happens, sure, but it's rare. I look at it like accepting a gig (or sales meeting, job interview, etc...). It gets entered on my Google calendar right away.
A while back, a band leader called me on my way to a gig and asked, "you ARE going to be here, right?" Turns out the very young, very talented drummer he he'd hired "double booked" an indoor, air-conditioned job over our hot-semi-outdoor one. Mistake? Maybe. But that band leader hasn't hired that drummer again.
Recently, a guy wasn't on set a half hour before downbeat. BL called him and was told he was on his way. Then he turned to me and said, "I think he forgot". Guy showed up 5 minutes before downbeat and made it just in time. Not sure what happens with him going forward, but if it were me, I'd definitely give him another shot - he did make it on time. But not my circus, not my monkeys - I love doing sideman work because things can happen and all I have to do is sit on the sidelines and await further instructions. So rigid? Maybe not so much.
No judgement of those who don't share my same view of the value of my time, it's just I know where my boundaries are and I'm not going to sweat or participate with those whose views are in collision with mine.