A musician is considered professional the moment they accept a paycheck, just like an artist or athlete. Some say they are semi-pro if it's not a career, but they still charge professional rates. It is common for college students teaching music lessons to charge the same as "professional" teachers because the industry considers them to be professional. As for not knowing what they are doing, orchestral musicians, especially string players, often have a decade or more of training before they can apply/audition for college/conservatory. Personally, I had 12 years of training with three instructors plus youth orchestra which requires separate tuition from private lessons. A college-level music student is highly competent. Some of them are better than some of the experienced professionals who haven't continued their education because it's fresh, and in music you lose skills if not practiced.