The authority, role, and power of Private Security Contractors vary greatly depending upon the State, Client, and Certifications held. They range anywhere from the pimple-face mall-rat with a walkie-talkie to highly-trained operators with extensive experience.
Many Private Security folks are armed officers who are protecting our federal, state, and local gov't institutions - including military installations. In fact, the Federal Gov't relies heavily on Private Security Contractors to protect nearly all federal installations.
In many jurisdictions, armed security officers DO have arrest authority; many are off-duty or retired LEO/Military, etc. Some Private Security gigs at gov't installations pay more than municipal and county police/sheriff's dept. Lots of Public Officers will transition to Private Security as the pay and benefits can be better than small jurisdictions can offer. Not every "private" officer is an untrained wanna-be working for minimum wage. In my area, numerous federal facilities (FEMA, FBI, IRS, CBP/ICE, Coast Guard) are staffed by armed Private Security Contractors who will affect an arrest and put you in cuffs in necessary.
In VA for example, all armed private security officers are trained, vetted, and credentialed by the VA Dept of Criminal Justice Services. They do have arrest authority - albeit limited to incidents on the client's (gov't/public or private client) property.
In regards to the incident above, I would need more information: What type of private security (armed or unarmed), what type of location (gov't, public institution, private business, etc), which state, what laws apply, etc?
The untrained dweebs with an iron-on badge at the bottom of the totem-pole who power trip on the public give the overall industry a bad name and (sometimes deserved) bad reputation. But do not assume that every Private Security Contractor is a powerless punk with no training, authority, or experience. Depending upon where you are, that kind of assumption could end in a VERY bad day.