since Russia will allow Israeli passport holders to visit Russia visa-free after Sept. 21, can someone who holds dual US/Israel citizenships take advantage of this?

here's an example..... "Joe" is a US citizen with a US passport. He checks in at JFK for a flight to Moscow. Can he just who the airline agent his Isarel passport? I'm guess he won't have problem with Russian immigration officials at Moscow airport, upon seeing his Israel passport. ]

However, when Joe checks in at Moscow airport for his flight back to the USA, he'll have to show his US passport... but then the Russian authorities will wonder why there's no Russian visa in his US passport, no? somehow I don't think the Russians will appreciate seeing two different passports? (if so, I guess the best work-around is to fly from Russia to Israel, then from Israel back to USA, no?)

Last, but not least, how will the US immigration officials react if Joe's passport has no visa/stamps for Russia?

P.S. why the heck can't the US and Russian sign a visa-free agreentment with each other? (ooops, I just realized how ridiculous this question sounds... hell will probably freeze over first... nevermind... )