It's to say, it's been a while since I've seen a Reptibreeze enclosure in-person, but if they're as flimsy as folks say, I'd say... (drum roll...)
it depends! (rim shot)
If one drills too many—or too large—holes too close together, it could affect the integrity (strength) of the frame, causing it to fail (buckle).
Screw size, number of holes, size of holes, condition of frame, load on the frame, yadda, yadda, yadda... are all variables. In some cases I'd go ahead and drill; in other cases I wouldn't—or I'd reinforce, or use another method.