Not true. No need to worry about this. On the day of the visa interview, just update the DS-260 info about other citizenships/nationalities, also other passports if your wife gets a Russian passport. Make sure to volunteer this new information to the document checker prior to the interview or to the interviewing officer at the consulate.
You will need to contact the consulate at Yerevan directly to request for case transfer. Chances are low that they will accept, given that your wife is just a tourist in Armenia and not a legal resident, but it wouldn't hurt her visa case to ask. From the Yerevan Visa Unit's visa navigator -- https://docs.google.com/forms/d/e/1FAIpQLSeTZcspb88FJZ1LE5QlHFqqc8TtAnrdR70K5BYbaqCs7uFfpw/viewform
IV - Transfer of Immigrant Visa case
TRANSFERS FOR RESIDENTS OF ARMENIA ONLY
At this time, Embassy Yerevan will only consider transfer cases for applicants who legally and physically reside in Armenia. Please contact NVC to consider your transfer request.
By the way, no US consulates in Russia currently process immigrant visas. Russians must go to Warsaw in Poland for their visa interview, or beg another consulate to accept their case.