I lost my password to go through the same process a few years ago, so I can confirm that yes, they do ask you for a lot of personal information. I did not get an email asking for it, I went to Skype's website to find support.
Fortunately my account was not in the process of being hacked, so I was more willing to provide information. Yet despite that, they would not provide me access to my account, and thus I have not used Skype since.
Fortunately my account was not in the process of being hacked, so I was more willing to provide information. Yet despite that, they would not provide me access to my account, and thus I have not used Skype since.