For land entry? Sure.

For water entry(via the river), not if there is navigable waterway to the entrance.

If they charge you money, they will be liable for accidents though. There's a law out there that will protect land owners who do NOT charge any entrance fees for activities such as cave diving.

If you are thinking about negotiating entry by land from a private party, prepare a waiver for the landowner so they can feel a bit easier about liability.