This isn't convincing. The farthest I will stretch out boarding is, the moment your baggage is stowed and you are seated with a seat belt fastened (as required

This isn't convincing. The farthest I will stretch out boarding is, the moment your baggage is stowed and you are seated with a seat belt fastened (as required by FARs), then you are boarded. In your example the basis for refusing transport is that due to an equipment problem it's not possible for that passenger to comply with FAR safety regulations and therefore is in breach of the contract of carriage for the airline. The terminology of the word boarding isn't even relevant in your example.