It's entirely possible to do what they wanted, but there's really no point in a crawlspace like that.

You just have to cut no more than 1/3 the size of the joist, and stay at least 2" from the edge.

This would require a lot of planning and redoing all the plumbing, but it's possible.

Most plumbers would probably say "sure, I'll do that but it'll cost you" cause this job would be a super pain in the ass.