Exactly right. Go to a "teaching hospital," which typically are the most revered such institutions--Sloan-Kettering, Cornell Medical, Boston Women's, etc.--and you will be operated on by a team of excellent students overseen by an excellent surgeon.
But ask me about my Sloan-Kettering prostatectomy 15 years ago and I will explain how my sex life was ended by a well-meaning student's "oops..."