For last couple of weeks I have been working with one of my clients who along with her daughter wants to go to St. Petersburg for a week. We were in the midst of planning when my client called and told me this story.
She met a woman who shared her experience while traveling with her child to Russia. That woman was born in the former USSR and her child was born in the USA (he is not 7 year old yet). Her US passport stated that her place of birth was Russia. She did not have a Russian passport and had no intention to have one. When last year she went to Russia with her child she was able to get into Russia without any problem. However on the way back, at the airport, a border officer stopped her and asked whether she was a Russian citizen. That woman told him that she was not, she was a US citizen. Then border officer asked her to present the proof that she renounced her Russian citizenship. Otherwise he could detain her for 48 hours and would not allow her get out of the country. He told that the child could fly back to the USA by himself. The woman was stunned. She called an American consul who came shortly. When the consul arrived he advised that nothing he could do. By Russian law if a person is born on the Russian territory he or she is a Russian citizen unless citizenship is renounced. Eventually the American consul helped her to get out from the airport and purchase a train ticket to Kiev, Ukraine, from where she safely flew back to the USA. Neither this woman nor my client (who was born in Moscow) would never go to Russia anymore.
I checked the State Department web site and it clearly states that if a Russian citizen wants to get out from Russia he or she needs to have a valid Russian passport even if US passport is present. Because by law, if people born in Russia are Russian citizens then it could be an issue for these people even if they hold US passports. From what I read it would not be so easy to get Russian passport for US citizens who don't live in Russia. It might take weeks if not months to get it. There are so many other obstacles that you can encounter: if you lose your American passport while in Russia or your visa expired or you are just switching planes to another country and so on. Just read Travel Advisory from US State Department. By the way, it is not so straight forward and cheap to renounce Russian, Ukrainian, and any other former Republic's citizenship.
I am sure that most people would not encounter these circumstances. However, would you go to Russia afterwards if you have similar situation? I don't know whether the same can happen if you are visiting Ukraine (if you were born in Ukraine) or Belarus (if you were born in Belarus) or any other Soviet Republic. All I know that I would be very skeptical sending my clients there.