Yes, but, at the same time, they're also not as legally protected as a government official/public servant would be. On the one hand, they are contractually obligated to observe the Constitution (never mind the moral, ethical, and for the city, political ramifications for not doing so), but on the other, they're simply private security with the authorization to carry firearms for self-defense only, and empowered by their employer to enforce certain, specific city ordinances, and to an extent, county, state and federal laws.
But, they are, at the end of the day, NOT a professional police force with the same tools and capabilities. The real danger is not that they "might not follow" the Constitution, but that they might encounter a situation that actual police agencies are (rather, "have been shorehorned into since the late 1960's") trained and intended to deal with. This includes everything from Active Shooters, hostage takers, Heat-style heavily armed bank robbers, terrorists, bombs, and, yes, melanin-enhanced individuals of lower economic strata deciding to "peacefully" make their "opinions" and "needs" known to the public (niggers nigging, rioting, and looting).
Additionally, if one of them has to deploy their firearm and use lethal force in such a situation, they wouldn't have the same protections as cops when it comes to the legal system. They are, specifically, not cops. Thus, their actions would be judged as private citizens acting in a law enforcement capacity as empowered by their jurisdiction. Would the city provide a lawyer if one of them has to put down a lumbering Harambe? Police Unions do. Could the city protect them from a law suit? Or their employers? Even frivolous ones that get dismissed still require the accused to show up, Lawyer up, and be prepared to see the enraged family Chimp Cage.
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