No. That kind of language specifies nothing other than that that kind of language was used. If a shell company was registered in Cyprus, the name of that shell/shelf would be available on the website, as is the case with Havelock's Panamanian shelf. Even a shell offers leads to investigators, hence no shell.
Stop believing everything you read on the interwebs.
There is no reason to pull the "Cyprus" name out of a hat when writing the terms and conditions. These things are written by lawyers and essentially mean "if you are going to sue us, you'd have to find a law in this particular jurisdiction that we have broken, because we legally reside (i.e., have headquarters or are registered) there".
Besides, Cyprus is the obvious choice when you want to register a shell company that does somewhat shady business. Gibraltar is another such place, but the Russians are well-known to have financial interests in Cyprus.
Also, I couldn't find a link right now, but there was some discussion about a prosecutor's office in Volgograd investigating the company (because Bitcoin was banned in Russia) and the admin of the exchange basically saying "we have nothing to worry about, we are registered in Cyprus and we aren't Russian citizens".
The reason would be that they are trying to misdirect governments and others who are trying to dissertation the identity of the operators/owners of btc-e.