There is a factor he's not accounting for with regard to the service academies. They can't offer athletic scholarships and are hindered by size restrictions - these are both true. However, these limitations are mitigated by two other important factors. First, they don't need to offer athletic scholarships because every student enrolled at the service academies is on full scholarship regardless. And, following from that, the service academies aren't bound by the 25 annual and 85 overall count restrictions on athletic scholarships to which every other FBS program has to adhere. In other words, they can effectively sign as many incoming recruits as they want. Army, for example, announced a signing class of 82 this year:
http://goarmywestpoint.com/news/2017/7/3/football-monken-welcomes-class-of-2021.aspx?path=football. Another issue is that they don't redshirt anyone because everyone (I believe) has to finish in 4 years, but again they try to overcome all of these hindrances with volume.