I'm not sure if you are aware, but there is a very new method that people are using to recover Skype accounts. It goes beyond the basic social engineer that was being used before. Simply using fake details on Skype is not enough to prevent your account from being compromised.
My Skype had an email that was 100% secret, fake billing information, fake name, fake everything. I also visited Skype support and asked them not to change the registered email on my account under any circumstances. They said they made a note on my account.
I was still hacked.