"Show me a law that says they are allowed to search me."
Look up "shopkeeper's privilege."
"They can of course declare me PNG."
From what you subsequently wrote, I'm sure you have.
"When approached by someone in Loss Prevention my first response is always curt "Request Denied" and I keep walking. Most of them are clueless enough to not know what to do next."
And the ones who do know what to do next have detained you and sent an information copy of their report to the police, and then PNG'd you out of their establishment. You probably have an extensive file with the local police department. You can reasonably expect that any police stop or police call involving you will not go well for you to begin with.
A competent LP person is quite rare these days, the industry is forever whining about its turnover rate. Most LP personnel are ill trained short timers who back off rather than risk a lawsuit. They know full well that their employers will hang them out to dry if they make a mistake.
That said, I try to accomdate them reasonably, such as doing the exit check at Sams Club, but beyond that I have little patience for some of the games I have seen them play.
Similar discussion here, with both points of view represented http://www.ripoffreport.com/reports/ripoff75454.htm
For the record:
- Never been detained
- Never been declared PNG
- No police file