The guy could have also been in the National Guard. As clarythedrill pointed out, promotion timelines used to be slower, they were even slower in the Guard. In the mid-90s, I had a soldier who was an E-4 Specialist with at least 10 years in. I suspect he had been busted back a time or too but I didn't really know. I also had a Vietnam Veteran E-6 in my platoon with at least 20 years in.
Also, if the guy was a Guardsman, the reason he would have listed 6 years of service is because you need 6 "Good Years" in the Guard to be considered a "Veteran" by most programs. I haven't looked it up in a few years but I think the Texas standards are 90 days of Active Duty while the Federal standards are 180 days. Anyway...
It may just be that they guy wants to be upfront and honest about his military service. When you're applying for jobs, a lot of companies want to know if you're a "Veteran". Probably more companies nowadays than wanted to know 15-20 years ago. In the 1990s, they just wanted to know if you were a "Vietnam Era Veteran" since that was a protected employment class.