This isn't quite true because in most real world scenarios, one of the requirements for code to be correct is that it provably halts in a fairly limited amount of time.

Not at all, it is saying that if the only things this service is providing is a human doing SA (since they dont have any deep-knowledge of the codebase), then you could just use an SA.

Code review in the real world misses the Halting problem, the only way you can really see it is if you know the codebase well enough to SEE it, and any 3rd party that is given a pull request to complete in a timely manner will not have time to fully learn your code base or even the modules you are submitting.

A human being doesn't solve the halting problem either.

Ironically, it very seldom is.

It's Rice's Theorem which tends to get me in trouble!