Reasonable suspicion is indeed the standard, but it's quite easy to fabricate if you're literally just trying to detain someone and have no intent of seeking a warrant or pressing charges. I can't imagine they'd need to fabricate much for Oswald, whom they knew quite a bit about.

Certainly, the FBI to this day regularly engages in much legally sketchier behavior with much lower stakes.

Edit: cf their weird habit of actively encouraging children to become terrorists

https://theintercept.com/2024/01/10/fbi-sting-isis-autistic-...

https://theintercept.com/2023/06/15/fbi-undercover-isis-teen...

https://theintercept.com/2023/07/31/fbi-isis-sting-mentally-...

Even in legal theory, probable cause is not so well defined. In practice, a judge can be found that will agree with cops on whatever they say.

The legal system in the US rarely favors the little guy. Even if you have an ironclad case, the expense to sue isn't worth it.

Probable cause is a joke. It's incredibly easy to come up with a suspicion that someone is violating a law. That said, they don't need probable cause to arrest you, just to do so without potential liability. 99+% of people don't have the money, time, or connections to sue the police for probable cause violations, and even those that do likely won't win anything substantial unless there are several incidents.

Heard of "probable cause on four legs"? That's what sniffing dogs are meant for. They can use a dog to find a probable cause, and they don't need a warrant either. That's a carve out from the fourth amendment.