I think your friend might be confused with buried wood chips consuming nitrogen while composting, but, wood chip mulch on the top (covering dirt) wont harm anything and will do good.

Mulches are materials that are layed onto the soils surface where over time the Soil Food Web will work on digesting them, but will not start and utilize all the available soil Nitrogen as they would if that same material were to be worked (tilled) into the soil. Tilled into soil raw organic matter can cause the Soil Food Web to get busy to digest that stuff and in doing that they will, temporarily, use most all of the available Nitrogen depriving growing plants of any.

Yes. Just make sure it doesn't happen to be walnut trees.

Do you have access to other mulches? Because there are definitely better mulches for a vegetable garden than wood chips. I prefer a nourishing mulch that breaks down more quickly than wood products in my vegetable gardens---like compost, leaves, or hay.