I'm not sure that is true in general, but it is unfortunately true for the elderly in China - precisely the population they want to protect. They've sort of screwed themselves by not vaxxing the elderly at high rates.
Which raises an interesting question. In China they could make elderly get vaccinated. They close entire large apartment buildings with one person'a exposure to covid, bring them food occasionally and organize security and testing for those people. Why not go through and get everyone vaccinated? They are already monitoring their lives closely with Orwellian surveillance, why not just add on required shots on top of all that hell? I haven't seen that China disputes the usefulness of covid vaccines.