I have an omega 3513.50 (a.k.a. 375.0083) which is basically the same watch with a different dial, and it is double coated inside and out. The Omga database says it's supposed to be that way:
http://www.omegawatches.com/planet-omega/heritage/vintage-details/14657/
It says: "Scratch-resistant sapphire (anti-reflective on both sides)"
I wouldn't be worried. Apparently, these don't have an Omega logo in the center of the glass (...whose absence could otherwise be a tell) either.
Be careful when removing it. On mine, the previous owner tried this probably through machinated polishing, and it scoffed the inner edge of the tachy ring a little.
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