This doesn’t really affect me, but I’m following because I’m really curious. I’m down to one kid left, and she isn’t at that level.
The only thing I can speak to on this is wrestling at Wyoming Seminary and Blair Academy. Given that they are probably the best 2 HS teams in the country (not just among prep schools, among ALL high schools), I can’t imagine that those coaches aren’t given great leeway in who they recruit. I would assume as long as certain academic/behavior thresholds are met they get anyone they want.
That is almost certainly not exactly what you are asking, but I think it does illustrate that at least in some scenarios the coaches do have considerable pull. For colleges it is pretty well known what support means at different schools, and it is not considered in poor taste to ask a coach to clarify, i.e. what % of recruits at this level that you support do you get in (frequently the answer is 100%, but if it isn’t you need to know that).
Good luck.