Legally authorized does not mean Illegal in the way you are taking it, no.

Joel, I repeat, SS has no specific power over congress, I already gave you the actual text of their mandate. The US Capitol Police are charged with protecting congress, and yes they do have concurrent jurisdiction. If the SS caught in a phone call about a threat to anyone's life, same as any other LE, they'd contact the people who had jurisdiction, because we have jurisdiction for many reason, one of which is those people are best equipped to handle the problem, for Local LE 'equipped' means 'there and numerous' which is why they so often consult with federal agencies who have specific applicable expertise, this is one of the reasons for concurrent jurisdiction. The SS is not an omnipresent group of super-troopers. They're pretty small, every federal department has its own LE branch for that matter, from the VA to the US Park Police. They all have jurisdictions, they all can do like any LE and stop major crimes in action, they all can contact the LEOs who have jurisdiction, they can all, from local PD up, arrest under hot or 'fresh' pursuit. I hear your frustration, because if the case you offer as an example were possible it would merit frustration, but its not, hence my frustration at having to tell someone how jurisdiction works. This is not a debate over how it functions or should function, this is simple cold hard fact and your basically saying "Oh yeah, well if cops can't arrest outside their jurisdiction and see a crazed gunmen then they can't do anything", the n-teenth time I say "Yes, of course they can, the law totally permits this". Forgetting geography for the moment, any LE can arrest in hot pursuit or if they have a warrant (typically only in state) but any and all officers can always arrest someone using citizens arrest powers - that covers any felony in action, they can act if they witness a felony - when a cop from NY busts someone in PA for waving around a gun at a fair they were attending off duty, it just counts as a citizens arrest. This is done all the time, its the legal route for out of jurisdiction emergency situations. Of course SS has a big jurisdiction, they are Federal Officers, so hot pursuit is irrelevant in their case.

None of the current rules allow any absurd cases like you propose, the SS is not the agency responsible for protecting congressmen, that's the US Capitol Police and whichever other LE groups have geographic jurisdiction. This is totally unrelated to not bothering to call in a crime. So if the SS stumbles across a credible threat to a congressmen they can act as appropriate, but not because the person is a member of congress, they can do the same for you or me. LE, in any form, generally do not ignore felonies, this does not mean that they can or do send their own LEOs to deal with a case that's not under their mandate. If SS stumbles across a group threatening to kill me, my congressmen, and POTUS, but decides the threat to POTUS was unreal but the one on me and my congressmen was, they can contact our local PD and the US Capitol Police, that one of the two fellows involved was an elected official is relevant only because they regularly work in proximity to USCP. There exact procedure is likely to vary from LE group to LE group and based on the severity and immediacy of the issue. Almost like someone with common sense wrote the rules. Jurisdictional infighting is a real thing, but generally over-dramatized and hyped in TV and novels for, well, good plot. As things are, if a threat came down from them about a congressmen (or anyone else) fairly soon thereafter a local uniformed LEO would roll up to that persons house to make sure they were okay at that moment, because they are nearest, and with immediacy removed jurisdiction would be sorted out. And if the tumbled out to a terrorist hit squad in action they would do what any other LE would do, contact everybody, though I believe nowadays they would contact HomeSec who would do this for them and coordinate. This would generally involve local LE, because they have jurisdiction and lots of people and guns right there.

You are welcome to continue objecting to this, I don't know why or on what grounds, to the best of my knowledge this is simple fact and at worst a LE expert might adjust a piece.