Call your insurance company and explain. Is the psychiatrist an in network provider? If so, let them know that you specifically chose a doctor who was in network and you had no control/say over which lab the doc used.
Something similar happened with me when I had a colonoscopy. The doc was in network, but the anesthesiologist was out of network. When I explained what happened to my insurance company, they covered it as if it was in network.
“Life is not orderly. No matter how we try to make it so, right in the middle of it lose a leg, fall in love, drop a jar of applesauce.” - Natalie Goldberg