I think the issue is now coming down to caps staying on nipples. It's not just the caps- some times it's the nipples. I suspect that a lot of modern nipples are more tapered- so an ill fitting cap can be squeezed and put on. A good shape has less taper and the cap fits tight. There is also the situation of not first dry firing a cap on each nipple prior to loading the gun. The dry firing burns off any oil or grease- otherwise the caps might loosen and cause a chain firing.
In any event a horseman had a lot of bouncing around and the caps stayed on the guns. Southern cavalrymen carried a lot of extra pistols, 4 maybe 6. They would have just relied on their swords if the revolver was unreliable. Hauling around 6 pistols that didn't work would be pointless. And, as I said before, I myself cannot recall anything witten at the time about caps falling off THEIR guns ( maybe better manufacturing tolerances than today's clones) however I have read about the multiple loading of muskets, etc.
In any event, in answer to your question, I think the revolver was indeed reliable.
And, while I'm thinking of it- I can't recall any writings on the west where a situation with caps falling off the revolver's nipples is mentioned even though I have read about gun mishaps- a guy grabbing a rifle by the barrel and shooting himself, etc. Let's also think about Wild Bill Hickok. When he died he owned about 130 guns- he was sort of a gun nut. The cartirdge Colt 1873 Peacemaker was available. If there was an issue with caps falling off of the percussion guns Hickok would not have carried a pair of cap and ball pistols.
I had a Navy 1851 Clone that had a problem with loose caps- I tried a couple of brands- no change- then a guy told me to buy some decent nipples- never had a problem after that.