Generally, in order for an employer to be held liable for an employee's misdeeds, the employee must be acting within the scope of his employment. For example, if a waiter spills coffee on a patron, the restaurant would be liable as pouring coffee is within the scope of the waiter's employment. If, on the other hand, a waiter goes up and slugs a patron in the back of the head, the restaurant would most likely not be liable since punching customers is not within the scope of a waiter's employment. The FTCA works the same way.
Most states make it a crime to file a false police report. Here is an example from Florida:
817.49 False reports of commission of crimes; penalty. -- Whoever willfully imparts, conveys or causes to be imparted or conveyed to any law enforcement officer false information or reports concerning the alleged commission of any crime under the laws of this state, knowing such information or report to be false, in that no such crime had actually been committed, shall upon conviction thereof be guilty of a misdemeanor of the first degree, punishable as provided in s. 775.082 or s. 775.083.
So if a TSO were actually to file a police report and the video made it crystal clear that the police report was false to the degree that the TSO just downright made it up and nothing of the sort happened, it is possible that the TSO could be charged with a crime.
Most states also have a tort for malicious prosecution. Here is an example of the elements of the tort in Illinois:
A cause of action for malicious prosecution must allege facts establishing the following:
(a) the defendant brought the underlying suit, either in a criminal or civil judicial proceeding against the claimant, maliciously and without probable cause;
(b) the termination of the underlying judicial proceeding in favor of the claimant;
(c) some "special injury" or special damage beyond the usual expense, time, or annoyance in defending the underlying suit.
Swick v. Liataud, 169 Ill. 2d 504 (1996). Citizens acting in good faith who have probable cause to believe crimes may have been committed are not liable. Allen v. Berger, 336 Ill. App. 3d 675 (2002). To recover for malicious prosecution, the claimant must plead and prove special damages. Special damages are established by showing:
(a) evidence of an arrest (where a malicious prosecution suit is based on the institution of criminal proceedings, a claimant need not make a showing of special damage); Levin v. King, 271 Ill. App. 3d 728 (1995); Bank of Lyons v. Schultz, 78 Ill. 2d 235 (1980).
So, if you had been arrested or charged based on the word of a TSO and the TSO was lying and it could be proven that it was in bad faith, the TSO might be liable. To determine if the TSO would be protected by the TSA or by the contractor company rather than personally liable, one would have to decide if that act was within the scope of employment.
In suits where an employer is sued for an employee's actions, employers will frequently claim that the employee was acting outside the scope of employment if there is room for such a claim. This is done by the employer to get dismissed from the suit thereby avoiding liability. If it works, the employee is then on his own.
The law is that there are exceptions to every law, but that's my un-expert understanding of how it generally works.