I don't have a Mesh pc, but it's clear you're doing something wrong if you're considering drilling out rivets. Put down the drill and step away from the pc!
Have you taken both side panels off the case? At worst it should be held in with 4 screws. If you cannot see any screws it's possible the whole thing will just slide out forwards. I have read many case reviews, and it sounds like drive cradles and plastic mounting rails are becoming the norm.
If you can't work it out I'd just phone Mesh and ask them