Mostly true, but sometimes DAV's get discounts based on DAV card, and also the National Park cards for seniors or disabled. I do know in Oregon State Parks, for example, DAV's get ten FREE camping days and you need the DAV card to prove it the first time, then you're in the computer. And Oregon has some of the best campgrounds in the country.
And, to receive your NP Card for camping, you need to prove disability the first time too, and that DAV card will do it.
I have all three, and have occasionally gotten discounts based on DAV card and not my Ret ID ... so, if you're eligible, might as well get it.
Then it only remains to do your homework or ask when you arrive somewhere and see - all they can say is no ... and sometimes, you get surprised.
Discounts at movies, restarants, and other civilian vendors depend on DAV card sometimes. Some restaurnats have Veterans Day, some have DAV day.
DAV Card makes little difference in military installations, but in civilian situations, it will make less impact on your wallet occasionally and every penny helps.