Well, it goes one way, so yeah you can't have a mathematically verifiable certificate without asymmetric key-pair cryptography.

It's just that there's nothing pro-authority about making it easy for people to verify: "this data hasn't changed since the signer signed it." It's a neutral capability.

There are cases where we can and should blame technologists for building antisocial things that shouldn't exist, but I think that cryptography for the most part falls on the pro-social side of that spectrum.