Given the right circumstances, anything is possible but that doesn't mean you should plan for it. Chances are, if it was last minute I wasn't thinking about taking my regulator just-in-case.
I do agree with you that if you had your own regulator you may avoid the problem but then again, what if the operator doesn't have enough BCs or better yet the BCs they have use a different inflator hose than yours? Sure you could solve that by keeping either a converter in your reg bag or keep both style inflator hoses on hand but then we're just preparing for every possible scenario.
When ever I go on a trip, I take my scuba gear with me, in case I have a chance to dive. I do try to be prepared for every reasonable contingency. I don't bring tanks and weights, but I bring everything else I would need to dive, just in case I get a chance to dive. I guess if they run out of tanks or weights, I would be out of luck. I'm sure we could keep going back and forth over the what ifs, but I would rather carry my own reg, knowing I'll have a good, well serviced reg to dive with. I've heard too many horror stories about rental regs.
Ron