First, foremost, without some form of security involved, any person can just make up their rolls. True, it starts to become suspicious when they're always rolling crits, but the point remains. Beyond that, incorporating dice into an online format is always tricky business.
To easily fix this, get everyone to sign up to a site
like this and start an E-tabletop session. The GM doesn't have to be present for people to roll dice in a session, and since it's publicly viewable and the text messages are not editable, whatever you roll is permanent. So are any rerolls you might do. Resolves the trust issue by removing trust from the equation.
What if the description of the action was really really good, but you fail the roll?
Then you've just learned a valuable lesson: The Dice Gods are a fickle people, and you should never presume to know what they're thinking. Always roll before you make the description. (ex: "She charges valiantly and swings her blade!...
*Rolls a 1*... Only to trip over a rock, hitting the ground with a horrendously deflated ego.")
Moreover, what if the target is bound and gagged, unconscious, totally restrained and your character is an expert marksman? Should the dice even allow for failure in such a situation?
Depends on the GM/player group, but generally there is such a thing in most systems as the free pass. Ever since the first D&D DM manual made the first rule "have fun and break any rules in order to do so", if rolling dice would make little sense in the given situation, don't bother. If a target is bound and gagged and unconscious, feel free to just let the player get the executioner's blow. If you want to represent a fight between a hardened veteran and a nooblord peasant, just add a custom modifier of your choice on all their rolls. (ex: In a D20 system, I'd probably add +10 to all the vet's rolls, or -10 to all the peasant's rolls.)
It's always about having fun, first and foremost. I find dice systems are most effective with a GM who understands that dice are a guiding compass more than a hard rule. If the Dice Gods sayeth "rocks falleth and everyone dies" you can always look up at the Dice Gods as the GM and say "nope. OVERRULED!" Combine with healthy communication with the players and you have a solid system.
I'd say the worst part of a dice system is probably the people that it can attract: Rules lawyers, min-maxers, twinks, et cetera. It's the same bizarre phenomena I often encounter with science fiction: Hard liners who are willing to sacrifice fun or even common sense in order to enforce their version of a fantasy. "You can't deflect that, that's not allowed according to paragraph 3, page 153!" It also doesn't work well with people who need absolute, complete control over the fate of their character and cannot tolerate them being injured without them desiring it. In an RP I recently put out, had a player honestly quit from the Interest Check section when they realized dice were involved and they could die, but hey, that player was honest about what they wanted, so kudos to that chick.
In Essence: Dice are the mechanics to make a story a little more unpredictable. While it seems like it's impossible to predict the results, it's not with a little bit of statistics and custom modifiers. So I guess the real barrier to entry is "can do you basic mathematics?"
