Revolvers actually have less maintenance than semi-auto handguns; for the most part they only need the barrel cleaned and a drop or two of oil every once in a while, while a semi-auto needs a partial disassembly to clean properly. There's also a lot more that can fail on a semi-auto. The real clincher in this case though would be the ease of swapping individual bullets, since you don't need to unload an entire magazine to swap just one bullet, and there's no worry of losing the magazine in the process.
Also, a six-shooter wouldn't really be lacking in capacity compared to the 7-round capacity of the Desert Eagle being brandished.
What I found problem with is him saying he wants a double-action revolver and then describing the operation of a single-action.