> Writing a Typescript program that takes external input but has no runtime error checking is already a mistake, though.

If it's a service, yes, and that's true no matter what technology the service is using. If it's a library, no, because...

> and if you write type assertions without ensuring that the assertions are accurate, then that's on you, not Typescript.

That's on whoever is using the library, not the library author. If the library author provides type definitions, and you as the consumer choose to ignore them, then it's on you.