It is clear that the three Elven rings were not made by Sauron. The inscription on the One Ring, made by Sauron, was in some way related to its power, even if we cannot say if it was by fancy (it makes for a nice trick :) ), if it was required by the spell or whatever: it is just like that. What is clear is that when Sauron put it on and the Elves understood the plot, a lot of action started rolling.
Now my point is: the ring poem (while being great, of course) seems slightly inaccurate.
We know that it is a verse "long known in Elven-lore", as Gandalf explains to Frodo in Shadows of the Past.
Was it written by the Elves? Why am I even asking, since Elves clearly love poetry and songs? Because:
- It explicitly mentions, at least two times, the (translation of the) evil inscription on the Ring.
- It is describing the actions and the purposes of the Lord of the Rings: but the Lord only gave out the Seven and the Nine, but not the Three which were exceptional: he had power over them because they were "made" with the same techniques but he had not planned them, they were made independently and one can imagine that they "caught him by surprise".
So, isn't it a bit strange that the verse long known in Elven lore seems to place the Three on the same footing, as if the purpose of the One Ring had been from start to rule them all? Isn't a bit strange that Elves used for their verses the very words of the spell (which were surely regarded as very evil: in our world it would be similar to quote in a poem words spoken by some dictator...)?
P.S. Yes, it is conceivable that Sauron would make some rings for the Elves, to keep them under his control: but this still had not happened and things went in a different direction.