I think you are just basing this off pure speculation.
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Saruman has long studied the lore of the ring-making of Sauron.
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Just because he studied it for many years doesn't mean he totally figured it out.
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With his own version of a home-made ring, he was able to muster an army of Urukhai, orcs who can travel at great speed & are not hindered by day light, not like your ordinary morgoth orcs. But then again, I cannot supply with a quote so you believe it or not, though I highly doubt Saurman's ring is nothing more than an ornament.
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It's not even known whether Saruman mixed orcs and men to get the uruk-hai, it's assumed and probably the likely choice, but it's not certain. So, I doubt whether there's any mention of Saruman's ring inabling him to create the race. Also, with the ornament comment, Saruman was from Aule, like Sauron, both naturally being greedy.