It depends on both. Trust me on this one as I have relatives that Coach in High School and close friends at Poqouson, Southampton, and Hampton. The administration plays a part, but money, size, an opportunity play a bigger part and here is why.
At a school like Westfield, we are talking about 2500 or so kids. Think of how many teachers that requires in the school compared to Appo or Gretna. Lets say 650 or so students. We are talking about 3 to 4 times as many teaching positions at Westfield. It's pretty easy for a Head Coach to have 2, even 3 of his choices as finding a slot for them to teach and get paid is easier. The money and opportunity part rests in NOVA or a larger football school that has more population of people which means more boosters which is more money to pay the Head Coach.
Another example....take a school like Gate City in SWVA. Small in size, and they hire a coach a year or so ago that didn't have any say so on assistants. Gate City is a traditional power, but because the assistants that were there before the new coach arrived were not fired, then they remain. Being a small school, you can't as easily find a slot for the new Head Coaches OC or DC pick unless some other teacher resigns or retires, etc. This is where the opportunity part comes in.
If a smaller school like Appo allowed Doug Smith to bring two of his choices with him, its the exception to the rule at a small school. We're two previous assistants fired which opened up two slots so the new assistants could be employed and teach? Or, did 2 teachers in the school resign, move on or retire which would have opened two slots allowing the administration to easily tell Smith, "you can bring two." I can bet you it was one of the above scenarios. Again, smaller schools simply don't have as many teaching positions in the school compared to larger ones. Smaller schools don't have the funds to simply "create another teaching slot" without some other teacher in the school either retiring, getting fired, or simply moving on. Administrations, even at smaller schools are usually very open and accomodate a new Head Coach in bringing one or two of his personal choices as assistants with him IF there are slots available to teach. Much of this at smaller schools is about timing and luck (who's retiring or moving) etc. The larger schools don't need as much help with the timing or luck part in hoping 1 or 2 teachers in the school either transfer or retire, thus opening two slots for the Head Coaches personal choice for assistants because.......this happens every year at large schools. This is not the case as the smaller schools, especially in SWVA where the economy is tough and jobs are not as easy to come by. The money part comes into play at larger football powerful schools that have hundreds of active boosters that can simply pay the money to create a new teaching slot allowing that assistant coach to get paid.