Not to justify trespassing, "urban exploring," and dangerous stunts one iota, but IF the property in question IS owned by the state, Feds, city, county, etc., then technically it may well partially "belong to them."

And before your head explodes at this rationalization, consider how I'm supposed to visit a state or national park or the Smithsonian, or that locomotive on display in a park with steps up to the cab, if it doesn't "belong to us."

Now, I agree that there's a huge difference between a park or museum that has been prepared for public visitation and an abandoned building or the like that has not been. And taking this rationalization to its "logical" extreme, you should be able to get in a transit or Amtrak locomotive and have a go at it.

So...using that logic, it's OK to hop the fence at the White House and take your own tour of "your" property?
You will probably get a free tour of another piece of Federal property!

Using “I own a piece of this” will get you a FREE physical and sociological profile in Washington if you choose this path.
I had a client that wanted to see the capitol building after dinner one night in the early evening.
The guards let us in for a “look see” but just so far, we left and the gentleman decided that he would peak in the window along the first floor cutting across the grass, I urged him a very loud voice not to do it. He was from California and had not been exposed to the real and extreme security around Washington government buildings.
Well the “guards” captured us, discussed the situation with me and him in a separated format, almost let him go until he explained that “he owns part of the building” as a taxpayer. He was escorted into a police van shouting and screaming as they drove off. I was told that I could pick him up at a defined location in about 3 hours. He was finally released about 2AM and had developed a full and firm understanding of what he owned verses what he thought he owned.
His boss called me in the AM, he wanting to know what happened, Capitol Police had called to verify his employment. Enough said!
We had business at a remote communications facility in Maryland later in the day, Security at that location assigned a guard to accompany us due to his statements the night before.

They're the difference between a secure facility and an abandoned building on a University campus. I want to explore an abandoned horse stable at my University only to be met by the police. The officer asked if I always wanted to private property at which point I politely bit firmly explained it that was State Property that it was unlocked and wide open and there were no signs for bidding trespassing. The officer realizing that I was right went on his way after running my ID to make sure that I wasn't wanted on anything. Also didn't thoes Sovereign citizens get away with occupying a federally owned building in a park

To boost the relevancy to rail preservation:

I have been made aware of at least three rail "preservation" properties where the very issues being described here--the gray area between "publicly owned property" and "quasi-private property"--has led to the problem of an inability, at least it is claimed, to post said "linear park" or "right of way," and even storage sidings, buildings, etc. against trespassing, in spite of (at least in the one case) a token lease of the property by a museum/railroad for the literal $1 a year. This has led to chronic trespass and vandalism problems at the one property for certain, and at the others I'm quite sure.

I know the reflexive response is "get your own railroad/property," but in these cases I can say that these museums/lines wouldn't/couldn't exist without the relative benevolence of the government owners of the properties in question.