Unfortunately it’s not his service that got him into Arlington but the fact that he was a congressman.
Merely being an elected official isn’t enough to be buried in Arlington. The requirements have been posted a couple times, or you can google them at “burial at Arlington.”
Not just any servicemember can be buried at Arlington. I’m not qualified, for instance, because I didn’t retire from the military, have the correct medals, or, obviously, die in combat. About the only way I could qualify to be buried in Arlington is if I later became an elected official of the US government. In that event, it would still be military service + being an elected official = Arlington interment, not being elected alone.