It's widely reported and easily believed that birds get a substantial dietary benefit from the many, many backyard bird feeders people put out, especially the seed-eating birds.
The Red-bellied Woodpeckers in my observations are a good example of that.
Seeds and nuts are not a complete diet, but counting the number of trips made to the feeders daily, they are getting substantial nourishment from peanuts, raisins and tree nuts.
Insects and invertebrates discovered naturally should complete their diet.
As for the 'red belly' he supposedly sports, I've only seen one Red-bellied Woodpecker, (a few years ago now), that actually lived up to his name.
Even then the 'red' on his belly came nowhere near the red on his head and nape.
This female had her turn at the banquet table, so now rests to digest.
I've read that European Starlings bully Red-bellied Woodpeckers for their nesting sites. I've also seen Blue Jays squabbling with Red-bellied Woodpeckers for food at feeders, but the Red-bellieds are getting their share, too.
Cornell Lab of Ornithology, All About Birds
The Sibley's Guide to Birds