I'm going to comment as if the same thing hypothetically happened in the US, because I have no idea what Russian contract law is like.
Regarding criminal fraud: That might be tough to prove. See, for example, this part of Virginia's fraud law:
http://leg1.state.va.us/cgi-bin/legp504.exe?000+cod+18.2-178
Note that merely obtaining a signature under false pretenses is a crime. Of course, the definition of "false pretenses" is the sticking point. Technically, the customer did not make any false representations. It seems he merely expected the bank not to notice his "proposed" contractual changes. That would not seem to satisfy the elements of the crime, though I wouldn't bet my own freedom on that.
Regarding bad faith: It would be interesting to see if the court would find a breach of the implied covenant of good faith and fair dealing. It's iffy. Generally, such a breach would arise from either party's conduct outside the signing of the contract itself. I.e. you do something underhanded to thwart the other party's enjoyment of his contractual rights, without breaching any specific term in the contract.
Could a breach of the implied covenant arise from the negotiation process itself? In my cursory search, I didn't come across any cases like that, but they could exist. In this case, there does seem to be some willful deception on the customer's part. One could argue, based on the circumstances, that he expected the bank not to notice his alterations. Perhaps this would be considered bad faith.
One could also argue that the contract is void as there was no meeting of the minds. This can be a difficult case to make when there is a written contract. Nonetheless, in unusual circumstances, which this appears to be, a written contract can be voided for this reason. Here, one could argue that the two parties thought they were signing contracts containing radically different text, and thus there was no meeting of the minds.
Note that you can't just claim this any time you want to get out of a written contract. The default assumption is that your signature indicates you read and understood the contract. You have to show some unusual circumstance--such as one party's surreptitious alteration prior to signing--if you want to claim there was no meeting of the minds. And even then, a win is far from guaranteed.