Would depend on what exactly 'vertical integration' is defined as. Most grocers' house brand items are produced by 'white label'/contract manufacturers that supply many different grocers. It's cutting one or at best two steps from the supply chain instead of true vertical integration.

HEB (the major player in the Texas market) is a notable exception that has true vertical integration, with in-house manufacturing and packaging facilities producing house brands, and its own direct relationship with raw goods/farm suppliers.