Incidentally, would that be the same Omega system where Captain Tracey found a way to live long and prosper? These single-Greek-letter designations are no doubt abbreviations - but in theory, there's nothing to say that this couldn't be the same system as in "Omega Glory", an episode without a stardate. If the Exeter
incident has not yet taken place, Kirk could easily overlook the goings-on on planet IV, as he enters the system with rhyetalyn blindfolds on. If said incident is in the past, ditto - and during the incident, Kirk would have had no reason to pay attention to planet III and the one hermit living there, possibly shrouded from cursory sensor scans.
Omega IV and "a small planet in the Omega system" called Holberg 917G. They could absolutely be in the same solar system.
Flint would certainly have ignored the Exeter and Enterprise in "The Omega Glory," and Kirk et al might very well not mention the Yangs and the Combs in "Requiem."