While technically and theoretically possible, that is absurd. Only the most foolish law enforcement agent would consider such a thing if the only reason was because an individual was "reported as being possibly scarey or annoying". Neither of those are a crime under any circumstance, nor is either of them worthy of investing tax-payer money enforcing. Get real... please.
Edit: Here's the actual law of trespass for places open to the public (like a Walmart parking lot. It appears that they can ask you to leave but the threat of arrest is still at least 24 hours away.
Private Property open to the general public
L.A.M.C. 41.24 (d)
applies to property open to the public, such as mini-malls, offices, businesses, etc. Under this section, the property
owner, agent or tenant can tell a person to leave and not return
ONLY if the request is rationally related to the type of services
performed or the facilities provided. Under this section, a person
can be asked to stay away for 24 hours. If a person refuses to leave
or returns within 24 hours, he or she can be arrested for a violation
of L.A.M.C.
41.24 (d).