I am with you on this logic Alex.
It would seem logical that the greeter at WalMart (or the barista at Starbucks) cannot create store policies. However, there is a group on OCDO that will chime in that ANY employee is a representative of the owner and therefore is empowered to trespass you. A couple of them will claim to be cops and insist that the greeter will have the power to trespass you if you take another step in after being warned or attempt to advise them that the store does not in fact have a policy prohibiting open carry of firearms. My initial reaction will always be to smile and question whether that employee is sure of the "policy" and request a member of management to verify that. However, if it begins to escalate, my thoughts are to back off to the parking lot and call the business on my cell phone and ask to speak with the senior manager on duty then continue to document what happens.
While Starbucks has a policy saying they support gun laws in their area, people still insist that the guy cleaning the bathroom can trespass you just because, well, just because. It doesn't make sense to me and I question some of the claims made from a practical viewpoint. There is also the aspect of the LEO who arrives to find an employee saying one thing and joe blow customer waving his piece of paper he printed off the Internet describing the actual business policy.
The cops I have talked with indicate that the law is indeed vague but that their reaction would be to seek the senior employee or manager on duty and sort it out unless they arrived to find a scuffle or other violent confrontation in progress. Part of the confusion when people from other states weigh in on this will be that in some states walking past properly posted signs does trespass you immediately. My understanding is that our state does not 9instantly trespass due to signage) and this seems borne out by the encounters described and the couple of times I have had my business rejected.
Good luck getting it sorted.