It could be an independent thing but it just reeks of that culture practice used in roman and egyptian times of elevating some great man e.g. emperor to the status of a god and having them be worshipped as such after death, and makes sense in terms of continuity that it might have just been adopted over inventing the same concept in the same part of the world around the same time but somehow having this be a purely independent invention. Society was already socialized for this sort of thing and support the political control of their own leadership through deep cultural ties like making them a seemingly unassailable part of the religion or some unstoppable force of nature.

Religious groups other than Catholics with few plausible connections to ancient Rome have independently conceived the idea of the importance of things like relics (e.g Buddhism), but it's called the Roman Catholic Church for a reason...

Of course the buddhist and the classical world were not so separated as people assumed, there was a period of cultural exchange after the conquests of Alexander and resulting greco-buddhist rump states.