I can't say how it might be organized elsewhere, but my friend is the LP Supervisor at a local Wal-Mart and one of my sons worked LP there for a couple years while in college (he left for another job less than a year ago).
Loss Prevention does answer to the local managers here. While they also have a regional director they must report to, the store manager does have control over customer apprehensions and trespass notices. And, most contacts with those committing shoplifting or attempting some sort of fraud (as this appears to have been assumed to be) result in a trespass warning. Few contacts result in a call to the police, but even if they do, and no arrest is made, Wal-Mart tends to issue the notice all the same. I cannot recall a time when the police were called that a notice was NOT delivered even if no charges were requested or no case could be made.