It's way worse than that, really...
The first time Kirk tries the proximity blasts, the two ships are basically at point blank ranges, dancing around a comet's tail while apparently moving at walking pace. Kirk never quite scores a proper hit, but a glancing blow (however that works with phasers) kills the Centurion. A stroke of luck can probably be excused there.
However, the second time, Kirk opens fire after just having spent a couple of minutes flying away from the target at the very highest warp speed his ship can possibly muster. The distances should be in excess of ten million miles at the very least, that is, assuming that Kirk can barely make lightspeed. And probably billions of miles, assuming (as we apparently should) that his ship can really fly from star to star in less than a week when doing proper warp speed.
If Kirk can't score a proper hit when he's a few hundred kilometers from his prey and the prey is making a hole in cometary gases, then him scoring a hit from a distance a billion times greater indeed has to be "the wildest stroke of luck", as Stiles puts it.
Except, of course, our heroes don't really have to count on luck. The ship may be invisible, but Spock has it on his sights all the time anyway. That is, as long as the Romulans keep moving. When they drift, they can't be aimed at; when they use engines, they can be aimed at, even if with a slight loss of precision. And this slight loss need not be proportional to the distances involved at all.
Timo Saloniemi