Currently, in TNAS status (at least in Northstar MLS), inspections are unable to be scheduled, but the intention of the status from the listing agent's perspective is only to block showings, not inspections.

"Please update the system to allow for Inspections and Walk-through during times when a listing is TNAS for Inspection or Statutory Recission or Other. This is the most frustrating thing!! When a seller wants to stop showings during a contingency, you require them to go "TNAS" status rather than pending inspection or pending other, etc. Then you also require them to sign a doc. After doing all of that, you disallow them from scheduling inspection. It's the most frustrating thing to have to explain to sellers why suddenly they can no longer see the name of the inspector or the request to inspect their home. Then we get calls from inspectors that cannot schedule. It undermines the whole process.
It would be great if you could fix this issue as the home is only UNAVAILABLE for SHOWINGS, not unavailable for inspections or walk-throughs."