Consider Raj Chetty's work; he shows that the primary determinant of student performance is intrinsic student qualities, but that teachers also matter a fair bit.
http://www.rajchetty.com/chettyfiles/value_added.pdf
http://www.rajchetty.com/chettyfiles/w19423.pdf
Why would you consider this factual claim to be an "incoherent position"?