Working for 13 years as an independent college advisor, I am often asked by families if they should still be working with their high school counselor. My advice is an emphatic YES.
No responsible private counselor should be telling students to ask for less help from their school. I may not agree with a high school counselor's college recommendations or feedback on an application, but that is the point: when a family gets plenty of feedback from many different sources that gives the family plenty of options. I always tell my students that I am their advisor and they are free to accept or reject my advice. I don't take it personally if a student doesn't agree with a college recommendation - in fact, students should fall in love with some recommendations and not others. It's healthy.
Bottom line: helping teens succeed is everyone's business. We should all be working as a team to help college-bound kids have the greatest opportunity - and that means private and high school counselors have important roles to play in the process.