So because I said that "the vaccines" themselves made the claims at immunity, you are interpreting that as false, based on the notion that the approval was not contingent on them providing immunity. This does not seem like a misunderstanding to me. It sounds like the painfully obvious interpretation of "Authority figures representing scientific institutions, with credentials, promoted these vaccines, claiming they would grant immunity." I think the only way you don't interpret it that was is if you are trying to obfuscate things (perhaps to yourself because recognizing corruption in scientific institutions is a direct attack to some people's egos and identities).