If a doctor writes on their website that they've never lost a patient or had an anesthesia complication can I trust them?

In my search of finding the right surgeon for a nose job in my area, I found one with 31 years of experience who has done at least 3000 noses. He has mostly excellent reviews. His website says that thanks to the fact that he is selective in making sure patients are healthy he's never lost a patient and he and his anesthesiologists have never had a complication. However, I saw that one of his anesthesiologists has a malpractice suit. I'm taking this seriously since every surgery has risks.