I think that is correct as well, brokers usually hold them in street name, once you have the cert no one can really do much with your shares. Those shares are no longer in your brokerage account, hence a broker cannot sell them. The transfer agent should also remove them from the pool of shares the DTC uses as well, I believe.
From my experience with DRPs, I actually had to deliver shares to get them reflected in my account to be able to sell them. DRPs are usually handled directly by the transfer agent, but I believe the process is similar.
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