This is not correct. I live in Moscow and have had visitors many times who used a hotel invitation to get their visa and then cancel their reservation, without any problems leaving. The one problem you might have is with "registration", which is required if you are in Moscow more than 72 hours. The hotel usually provides the "registration" stamp when you check-in (although there are other sources-- see www.expat.ru for more info). Without registration you could be hassled and/or fined by the police. But the passport control officers who process you at the airport are have no authority to ensure you have registration (only the police do) and therefore cannot make any problems for you upon exit. (They may try, but I have not seen that happen in a long time at major airports and like sheremetyevo or domodedevo. It is more likely to happen if you go through some out of the way airport where the border guards dont often see foreigners and there is little control over them).