No, indeed, they do not. In fact, the amount of OAS they collect is determined by their other forms of income, because if they are totally self-supporting, then they are entitled to either a lot less or some less OAS support. It's designed to provide a certain standard. Beyond that, if a person is receiving it through other sources, no, they're not entitled to it, and certainly not to bank it for the future.
On October 28th, 2010. See this statement in context.