The shares are not in your name when held with a broker. The theory is that shares with brokers are mostly IOUs and were never actually secured.

Directly registering with Computershare transfers the share from your broker to a custodian (computershare) who holds the shares in your name. This forces brokers to actually secure the share and transfer it. It also provides full transparency to the company. Gamestop has started to disclose how many shares are directly registered in their quarterly earnings reports. Once a share is in your name, it can't be sold without your consent.