To a new Bombadil debate?

Well to make a complete circle then, and go back to from where we started the matter, was weither Firebeards and Broadbeams got Rings, which should point out they had Kings after their kingdom fell, which in itself I deem quite unlikley since the majorities of their populations lived under the king of Durin's line?
Could they if no kings got Rings anyway? Further concern in what parts of the in-world and IRL lore should be given graver weight and not.