Its been a while since I bought from the base (We now have annual pass) but in the five or six times I used Military tickets I have never once shown my ID card.
It's pretty common for military to get tickets for their family members, we do it all the time- if we are going to be going on the same trip, we don't just give out discount tickets for nothing, you know My Aunt and Uncle didn't have a problem using theirs, I think it's because the tickets are just regular tickets sold for less for military members, no mention of military on them. I'll be buying some for my In-laws for our trip in two weeks, hopefully no problems there!
No ID is required. We got military park hoppers a couple years back from my uncle who's son used to be in the military (R.I.P to him) and they didn't ask us any questions when we got through the gate.