I was sure I've heard of that story once before, so I googled it; and here's basically what happened:
Napoleon, apparently, did apply to the Russian army, sometime in early 1789 (so a bit before the Revolution).
He was of a relatively low rank then (naturally), and wanted to get at least the same rank in the Russian army.
However, around the same time as his application, there was an order from Catherine II saying (in effect) that the Russian army has enough foreigners in it already, and any further ones will be at least one rank lower (than they were in their original army).
The order arrived to the army headquarters several days before the application; so Napoleon was turned down with words to the effect that, um, sorry, the order. The rest is history.
(He applied again in 1792, apparently; that was also turned down, and might have been affected by the Revolution. I'm slightly more hazy on that part of the story.)
The POD is then obvious: have that order arrive (and/or be issued) a week or two later. It's actually a pretty clean POD - not much will really change by this little difference except for the Napoleon story.