Not sure if thats what they are trying to claim. The VA police and OU police patrol the lot. I remember several years ago at orientation they said it was a no no. Thought with the newer ruling things might have changed.
They are govt employees that are LEO's with authority even over OKC police etc when on VA property. When outside LEOs (OKC police for example) are at the hospital, they have to check their guns with the VA police.
If you're a .gov employee, the agency usually has a policy prohibiting firearms in vehicles if the lot is owned, subsidized or controlled by the .gov. It's a quick way to loose that .gov job. That's why I'm glad my employer doesn't do these things where I park. If they started, I'd find a different place to park.
I don't believe it's considered federal property unless they own it. But that doesn't mean you might not run into trouble.
I work for the Fed. and if it considered Fed property no weapons of any kind. That includes large knives too. Anything larger then a small pocket knife. Firearms are a big no no. Where I work a firearm in the trunk would most likey get you fired.