When you did your military training you increased your reps via endurance training, which is very effective apparently. That doesn't mean heavy weight training won't help increase reps as well. Strength and endurance combo is the best. Without enough strength, you can't max out your muscles true endurance. By that I mean, when I was in middle school, I could do like 22 pushups, I was a lurp. I could again do 22 pushups with 2 minutes rest, and again with 2 minutes rest. I just didn't have enough strength to really tax my endurance.
But do you believe that benching heavy will help contribute to the ability to perform more reps if correlated also with endurance training like you described in your military training?
I know for a fact that before I started lifting weights, I could do about 35 pushups, weak sauce. I hadn't done a single pushup for more than a year, and when I couldn't make it on chest day to the gym because of my uncle's funeral in march this year, I did pushups to subistitute, I did 82 pushups in one set, and did a second set of 60+. My pushups increased by more than double without every doing one single pushup. I trained in the 8-12 rep range on bench, with a few 4-6 rep sets once in a while.
Fact: Heavy weight training will help you do more push ups than before without ever doing one.