No doubt there are some HR/legal folks wanting to avoid the liability of 'training' someone on something that goes badly. The workaround to that is to have the training in an auditorium and not keep attendance on who is in the room.

or mandate the contracting entity do the training. I've seen that in places that tried to be equitable about the relationship with their contractors.

Typically the business gets billed for the privilege though

This is probably because the training costs money and they don't see the contractors as their responsibility.

Why would they train you? It’s the responsibility of your parent company and for all they know you’ve already been thoroughly trained for active shootings in numerous other companies you’ve worked at.

You are not their problem.

For something like active-shooter training, location specific details could matter. A generic training isn't the same thing.

Generic is good enough. Overtraining is bad.

As a hospital contractor, are you different than, say, the HVAC contractor that comes in to work on mechanical equipment?

This is why I don't even transit in the US any more. No holidays, no layovers, no work aspirations any more.

I was referring to the active shooter problem - to which I feel it is too risky to visit the US.

Well, employees are a liability for the hospital. You were not, hence no need for you to get training. It is logical. Ethical, up for debate.