Dallas writes:

So nobody's answered the question, is being listed in the registry
optional?

Apparently it is.

It's not optional. However, the SSN, certificate number, and date of birth of
pilots are not included in the public information available in the registry,
and pilots can request that their address information be hidden.

There would be little point to a registry that were not public. The whole idea
is to allow third parties to verify that a particular person is indeed a
licensed pilot.

I suspect that in this case the pilot may have been an unlicensed student
pilot (someone who had been taking instruction but had not obtained a student
pilot license yet), or his name in the database is different from the one
reported. There are quite a few pilots named Joe Stack.