I don't know how much research there has been on this, but even so individual exceptions are always likely to exist. I coached a girl once whose mother felt that since her daughter was not likely to become a "professional" at running that it was a waste of time and would only interfere with school. This girl was in grade nine. Turns out that this was more an indication of problems between mother and daughter eventually requiring years of family counselling, rather than a problem between running and academics.
Anecdotally, we all know (as others have said) of runners with high academic standing - but I would find it difficult to claim that running "leads" to high marks. Rather, some/many runners do well academically because the process and self-discipline inherent in training and racing mimics that of studying and exams. It is learning how to prepare in a consistent manner over long periods of time. In my coaching experience, particularly amongst girls, dedicated runners have often achieved high school averages above 90%, but not everyone of course. Within the confines of the school environment, being a part of a cross-country team can be a valuable experience socially and the exercise benefits are obvious. My question to the mother would be why shouldn't her daughter participate? This is a healthy endeavour, unless her time is already taken up by other priorities, and/or is academically challenged, in which this may become an additional unwarranted stress.
Parents must realize that if their child has that much difficulty with school and/or motivation such that all extraneous activities save for class and studying are restricted, then they are not really University material anyway! High school should not be that difficult for most.