Quite a pervasive myth this one. I'll just let a few quotes from a Horticultural Scientist - Dr Linda Chalker-Scott blow it out of the water. She is an Associate Professor in this field at Washington State University.
From a scientific viewpoint, there are few drawbacks to using arborist wood chips but many benefits. It mimics what you might find in the duff layer of a forest – which is really what we should be shooting for in many of our landscapes that are based on trees and shrubs. I can say definitively that if wood chips are used as a topdressing and not worked into the soil they will not tie up nitrogen. We’ve demonstrated this in laboratory research as have others.
.....many studies have demonstrated that woody mulch materials increase nutrient levels in soils and/or associated plant foliage. My hypothesis is that a zone of nitrogen deficiency exists at the mulch/soil interface, inhibiting weed seed germination while having no influence upon established plant roots below the soil surface. For this reason, it is inadvisable to use high C:N mulches in annual beds or vegetable gardens where the plants of interest do not have deep, extensive root systems
Another myth is that you must let wood chips age before you use them. Dr Chalker-Scott again;
Personally, I have never done this; I happen to love the smell of fresh wood chips and enjoy spreading them out over the landscape. Additionally, some of the nutrient value (particularly nitrogen if the chips contain leaves or needles) will be lost in the composting process. Using fresh chips ensures that some of the foliar nitrogen will feed the landscape rather than the compost pile