This is true, but we need more precise language for this. I am once again proposing "sovereign" as the opposite of "hashes someone else's template" while leaving "solo" to mean "doesn't share the block reward".
So:
- self-hosted Public Pool, CKPool, or datum_gateway without pool split = sovereign solo mining
- DATUM on Ocean = sovereign pool mining
- using the Public Pool or CKPool servers = centralized solo mining
- Antpool Borg = centralized pool mining