This is false because many fields do care very much. E.g. medicine (and not just mds), law, the patent bar, and many engineering fields care about accreditation. Even degrees from highly acclaimed universities aren't enough if the degree isn't accredted by the right body (eg ABET for the patent bar).
This is also not relevant because, in practice, places with good reputations are typically accredited.
I do think there are people that don't care, but I suspect they also don't care about the degree as well. They are more concerned about the real world performance of the individual. I think you'd be hard pressed to find someone in the above mentioned fields like that.
I also think that a Math degree falls into both of those "ideals", but more so on the side of accreditation is important.
But yes, there are a lot of jobs out there that even Stanford CS graduates aren't qualified for.
Note: the patent bar's eligibility rules have special exemptions for CS degrees that are not ABET accredited but do satisfy other criteria, so many Stanford CS graduates will automatically qualify for the patent bar based upon those alternative standards. But that doesn't mean the patent bar doesn't care about accreditation.
And it's worth noting that any institution with a half-decent reputation has some form of accreditation. Again, this was the second point of my post -- accreditation is actually does do a very good job at over-approximating the set of educational institutions whose degrees mean something.
