I've been directed by LEOs to render armed assistance in the past, and I would say that it is entirely the discretion of the individual LEO. I believe they are warranted to recruit aid at any time from anyone, but they are responsible at least in part for what then transpires. I discussed this with a Washington State Patrol Seargent once, and he put it like this: If he was chasing a bad guy, and he yelled at someone in the BGs path to "stop him", the person might just think that means to shoot the BG, and pull out his hand cannon and blow the man down. Now obviously the idiot that does that is going to go to court, but the cop may be standing right beside him in court when he does.

Anyways, I've received such direction from local Police Chiefs to Sheriffs to Military Police, and they pretty much all act the same. I am sure that it is predicated on how well they know the person they are ordering and whether they trust that person's judgement or not, and how imminent the situation at hand was. I can tell you in a firefight they are going to appreciate any qualified help they can get if it is going against them.

As to particular laws, well, I'd say what you found pretty much spells it out. That seems to be a fairly common position in most jurisdictions.

One other thing, don't expect a police dog to obey your commands just because the patrolman recruited you. As far as they are concerned, everyone not the patrolman is a bad guy, inlcuding other patrolmen sometimes (LOL)...