The theory--don't know if it's ever been tested--is that water lubricates things so a thorn or whatever that might have been stopped or broken off in the rubber slips through more easily and reaches the tube. I doubt it would have much effect on a thick car tire, but bike tires are so thin it wouldn't take much to increase the chance of flats.
As for actual numbers, my record is six on one century (the road was lined with thorny brush and it had been windy, so there were twigs everywhere) and NINE on my 22-mile round trip commute to work, from running over a shattered six-pack and picking up glass shards in both tires.