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-...