I understand it well. No you do not. The "probable cause" standard does not apply to merchants, depending on your jurisdiction, the standard is "reasonable."
You are quite correct there is a difference between reasonable cause and probable cause. The privilege and language varies from state to state and in common law. However, I do not ever recall seeing that storekeepers privilege allowed search or person or vehicles, only reasonable detention and recovery of property with limited hot pursuit. Also exercising it erroneously lays the merchant open for legal claims since the wording is vague.
Most LPs, even the few long term professionals in the field, can not provide a irrefutable definition of what constitutes reasonable or probable cause. Also none of their apologists here has asserted that refusal to show a receipt after having left the premises constitutes either reasonable or probable cause.
As for their LP limitations, here is a case that is instructive
http://www.aoc.state.nc.us/www/public/coa/opinions/2000/990996-1.htm
LP are like bounty hunters. They operate in a fairly gray area of the law. There is full support for them when they are correct but no protection when they screw up and go after the wrong person. Having been wrongly confronted I don't take any nonsense from them and press hard for consequences (either legal or more immediate) when they do. As BeHoldAPaleHorse pointed out they can generate police file entries on civilians without their knowledge or appeal. Its only right that they face unlawful detention, assault and other charges when they are wrong.