You can find the official rules here (point 13): rail.cc/en/interrail-rules
So, if your friend wants to travel with Interrail, he has two options in my opinion:
a) travel with Russian passport and write Russian passport number on Interrail pass
b) travel with US passport and write US passport number on Interrail pass and take proof of residency in Russia with him to prove that he is living in Russia. This has to be issued by a governmental body (registration office etc), mobile phone, appartment bills etc are not accepted.
Option c) would be to use his Russian ID card (citizen card) for the Interrail pass and take the US passport with him for border controls. However, this wouldn't be legal if he is living outside of Russia. Where is his current residency?
Anyway, it is unlikey that a train guard would ask for his (US) passport as long as the number printed on the Interrail ticket is the same as on his Russian ID card. Also, I dont think that a train guard has the right to ask for his passport as long as he has the ID card with him, but on the other hand the Russian ID card is not valid for crossing borders in Europe apparently so it could be problematic sometimes.