I think the ‘best’ when talking about Andover/Exeter is related to their name recognition more than acceptance rate. They are the boarding schools people most likely have heard of and are likely to be impressed by, if they know any boarding schools at all. And they send most kids to HYP, which is the other thing people seem to really care about. Given their size the acceptance rate is higher than some smaller schools.
That is not to say I would ever advocate anyone to choose just those two schools to apply to (we did not even look at either) but that’s the justification people use when they make the call that they are the only ones worth the money. The deadlines have passed for most schools now anyway, so let’s just hope OP may get in one of them. Sounds like she has solid local back up if not.