First, an excerpt from the Ayn Rand Lexicon entry on Anarchism:
Now imagine a private entity that specializes in some craft that requires the initiation of force, for example a professional bodyguard service. Said company is objectively operated, has some system of checks and balances on its own power, and has a record of initiation force only in proper circumstances (i.e. in self-defense or in defense of its clients).
Is this an example of an illegitimate private force? If not, how far can a self-defense business go before, as the quote above mentions, there exists a potential of abuse? (Abuse meaning the initiating of force outside the context of defense.) Does not a government have that same potential?
I think that a private company should be able to use force to protect a person or their property only to the extent that the person himself would be legally entitled to use force in self-defense. For example, if a private citizen notices that he has been robbed after the fact, he cannot legally use force against the person who he thinks robbed him--he must resort to the courts so that the dispute can be resolved by objective rules of law. Thus, it should also be illegal for his private security force to use force against the alleged robber. On the other hand, it is permissible for a private citizen to use force to stop an assault in progress. Accordingly, it should be permissible for the citizen's private security force to use force in that circumstance.
Binswanger's quotation against the private use of retaliatory force is a statement of the general principle articulated by Rand that a government must have a monopoly on the retaliatory use of force, and I agree with it wholeheartedly, but the quotation cannot be regarded as an absolute out of context (of course the principle is an absolute within its context, but the single statement does not include within it all the complexities and details that may go into the context). Rand acknowledged the rights of the individual to use force in self-defense where necessary (i.e., where the threat of harm is immediate and one cannot wait for the government to protect you). This is clearly an instance of private force, which Rand sanctions. I believe the reasons that justify the private use of force by an individual equally justify the private use of force by a security firm.
As far as the question implied in your comment, I do not think that the mere existence of a private security force (be it 1 man or 50) constitutes a threat to others, let alone an objective threat of the kind rising to the level of a rights violation. It is certainly possible that the security force could be used to harass, intimidate, or threaten people, in which case it would be violating rights and it would be proper to stop them. However, this is not inevitable--the mere presence of armed men is not a threat.