Well, I always took the song as Woody pointing out that, while the rich lay claim to huge swaths of the country, that it really belonged to all those who laboured so hard to build it. The "no trespassing" verse underlines that to me.
For another perspective, when I was part of a community song group a
number of years ago, we had environmental activist members who said we
shouldn't be singing a song that made any claim to "owning" the land.
I thought that they missed the point, but I guess it's all in the ear of the beholder.