The proposed OSHA order is satisfied by getting tested. If the employee CHOOSES to get the vaccine, that's up to the employee. The states can pretend this is a vaccine mandate, but it isn't. What if the order just required testing? If that would be OK, how can an alternative (vaccination) make it not OK?

The law looks only at the easiest form of compliance, not the one that gets the most news coverage or is the most invasive. The other option, in this case, vaccination, is just an additional option for the employee that has no bearing on the legality of the order.