JdeBP> "Split horizon" DNS service is the only case where the idea
JdeBP> of multiple namespaces actually has meaning. Every entity
JdeBP> only ever sees one DNS namespace. That's the way that DNS
JdeBP> works. "Split horizon" DNS service is where different
JdeBP> entities see different namespaces.

HM> No, this above incorrect and likely based on a
HM> misunderstanding of the term "namespace".

As I said, this is the meaning of the term from RFC 1034 section 2.4.

HM> A split horizon may nor may not be associated with a separate
HM> namespace (e.g., private vs. the Internet namespaces).

"Split horizon" DNS service is always associated with multiple namespaces.
The whole essence of "split horizon" DNS service is that different entities
see different namespaces. However, even in "split horizon" DNS service there
is no "checking a second namespace" that occurs. Different entities see
different namespaces, but no individual entity sees more than one namespace.
That's simply not the way that DNS works.