...Based on what is that part about the sign (placed by the owner/proprietor) already having "denied entry" not valid? Is it the wording of the sign? Or just in general. I guess my question is if that line establishes some legal standing for the sign, where is the legal standard that it doesn't have any weight?
A "NO GUNS" sign does not deny entry like a "NO TRESPASSING" sign would.
If that were the case, not wearing a shirt or shoes would also become a crime some places rather than simply a reason to refuse you service and make you leave.