I don't know the statutes offhand; I'm basing this on what I was taught in my CCW class years ago.

The general idea is that the state sets limited laws on where you can't carry concealed. Government buildings, etc. These restrictions hold the force of law. For a private property owner, they can certainly say "no guns," but it has the same legal weight as if they said "no hats." They can set rules for their property, but those rules don't magically become law. That's where trespassing laws come in; if you're asked to leave, they have the right to ask you to do so.

Some states do have laws in place stating that "no guns" signs are legally binding, but the signs must meet certain legal criteria as far as wording. Surprisingly, I think Texas is one of these states, but I could be wrong.

My state is solidly blue, so it does seem strange to me that the laws are written as they are.