I'd actually guess you're less likely to get a flat on gravel. Gravel = less traffic = fewer people throwing bottles and trash out of their car windows. Also, any shards of glass or metal will settle to the bottom, underneath stones, rather than sitting on top stalking your tires like they do on asphalt.

Now, handling a skinny tire, stiff frame road bike on gravel is its own special joy, and I personally HATE it and avoid it whenever possible. But flats aren't the reason.