Wider tires = less flats?

This seems to be implied in a lot of the posts.
Is it really true, or is it more connected to tire quality? I poked around Sheldon Brown's site, and despite an extensive discussion of tires he didn't mention any correlation between tire width and getting flats.

If it's generally found to be true, does anybody know why?

I ride on 700x25 tires and though I like them fairly well, I get way more flats than I'd like (which has been 4 or 5 in the last 3 months). Would going up to a 32 or 35 help?

Thanks!

Seth