Hmm... NO. As long as they are working under my license (i.e. direction or supervision), their privileges end where I say.
Sort of. If they are credentialed to perform a procedure in a hospital, they aren't working "under (your) license", but under their's. You are responsible for directing the anesthetic care, but the ultimate answer is it depends who they work for. If they are hospital employees that the hospital says can do a certain procedure, well let's just say it isn't as completely cut and dry is if they aren't credentialed to do something.