I think this makes sense as a reminder of a thing that is true anyway, as you somewhat already said; but also consider situations like:
A given reviewer was only reviewing for substance, and the error is stylistic, or vice versa;
A given reviewer was only reviewing for a subset of the subject matter;
A given reviewer was reviewing an early draft, and an error was introduced in a later draft.
In general a given reviewer will not necessarily have a real opportunity to catch any particular error, and usually a reader won’t have enough context to determine whether they did or didn’t. The author by contrast always bears responsibility for errors.
I think the point of the caveat is that it is polite to thank people who helped, but putting someone’s name on something implies they bear responsibility for it, and so the disclaimer is meant to keep the acknowledgement from being double-edged in an inappropriate way. Someone familiar with the writing and editing process will already in theory know all these things; someone who is not familiar maybe won’t be. But ultimately I see it as kind of a phatic courtesy which merely alludes to all this.
Ultrapersonal Healthcare appears to have forgotten to pay Squarespace to renew their website, which doesn’t seem like a great sign.