There are many ways to verify military service. For example, all military personnel goes through some kind of boot camp. There will be graduation photos and records.
There is also the well known DD form 214 (or 215), which every service person receives that spells out their military record.
Most military personnel can confirm their service by their training schools and assignments.
For example, President Bush is a fighter pilot. The training for fighter pilots is extensive and well documented. He would first start flying trainers and then progress through various aircraft till he comes to the one he will be flying.
During this training phase there is extensive evaluations and reports. Training for the military is at well known military bases, so there's lots of ways to confirm someone was at a certain base, such as apartment rentals, car sales, restaurants and pubs visited.
Take Top Gun for example. Around the base there are several well known pubs where fighter pilots congregate, often with photos on the walls of more well known pilots and their planes.
Another example, most all Air Force personel go to boot camp at Lackland AFB, San Antonio TX. Navy has several boot camps, etc. Start with the branch of service and if the person started as an enlisted man or officer, then go from there.
All it takes is a little digging into.
Had several boot camps. Great Mistakes aka Great Lakes is the only one that remains open.