As an AR resident, I dont care if they can search me and my bag. If they are polite, they might get cooperation. If they come up to me like some mall ninja and want to harass me, they can bring in someone with authority, tact, training, and most importantly, a BADGE. A LEO I will cooperate with because he has the authority. Some oppressive mall ninja is going to be reciving all the crap he/she throws at me right back at them.
Having a right to question me does not add up to unlawful detainment. If they want to say that someone fitting my description ran off with a Dillard's bag when I am in possession of one and be polite about it, its kosher with me.
If some security guard walks up to me when I am entering the building and asks to search it, I will say no and leave. If they want to press the issue, they can call the cops and they will find out that I simply didnt want to be searched and peacefully left the building/premises. The security guard wants to get physical, they can have their desire fulfilled because they have the same right to touch me when I am being peaceful as any other Joe Blow in the mall. They wont like it either.
I am not for disrespecting authority figures. SO's have a certain amount of authority, which I respect as long as they respect my rights. Its within their perogative to ask me to leave when I dont submit to their search. Its within my rights to give the mall $0 and a hastily written letter dispising their business practices as well.