An attacker can still send a compromised payload if there's no signature verification of the update. It takes a more sophisticated attack (e.g. supply chain attack, hijacking AMD's update website, etc.) but it has happened before to other companies. If the payload is signed and verified, an attacker would also need to gain access to AMD's private key to successfully send out a bad update. Assuming reasonable security, getting that private key would be a lot harder to get on top of somehow compromising AMD's update web service.

Also CRC checks over the internet are sort of silly and redundant since every packet sent would already be subject to a similar CRC check and bad packets would be ignored (dropped and re-requested). It would only prevent corruption on disk or in memory which are a lot less likely than transmission corruption.