Interestingly, this has come up a good bit in the past in my group offline. Here with Roll20, we'll probably be using the /roll commands, but that is more so we can keep track of them in the chat logs. We'll be doing most of the added numerics by self-report, more than likely.
Offline, for years, everyone would get really paranoid about another player if they got a long streak of critical rolls, and people would go so far as to vet the rolls of anyone sitting next to them. Or to ask someone to do it. In my games that doesn't happen as much... We play for the story, and frankly, I occasionally do very unpleasant things to the characters that have no mechanics at all, so if they showboat a bit I don't care. For the most part, I just trust them.
But in younger groups... especially with hardcore videogaming types, people with serious eye-on-the-prize mentality or constant anxiety over character death, I'd keep my eyes on the dice. I suspect it is a trust issue in most groups... the system is there to handle the conflicts, so that everyone gets a fair shake. Often, circumventing that purpose seems like straight-up cheating. Else, it may as well be a story game (not that there is anything wrong with that).
Online can be different sometimes (not a concern here though). I used to do development on text-based Vampire: The Masquerade game environments, and I got my hands into someone else's code once (by invitation) and discovered his dice rolling mechanism favored any character with one of a list of names. All of them were his characters, some of which he used for ST'ing NPCs. Every time a die rolled a 1 after an initial instance, it randomly replaced the new ones with 2 through 5. He could fail, but he made it almost impossible for him to botch.
Trust issues. *shrug*
