David,
I quite disagree with that "common knowledge." If your property manager is unsatisfactory, you should replace them ASAP. I doubt a tenant will pack up their stuff and go to the hassle of moving just because the manager was replaced, and it may even be a relief. The tenant's concerns are quality of life, value for the dollar, and having their concerns dealt with fairly.
I also notice that you are referring to a tenant in the singular. I don't think you need a manager for only one property. You will find that you can manage multiple tenants by yourself with only a few hours per month of effort. Having a leasing agent and a handyman will save you a lot of time and effort, but that is a story for another time...
