Uh, that support person is giving you some incorrect information in places, or you misunderstood what they were advising.
That is the page for Activation Lock removal request service (and that URL you provided me renders it in Russian, I think). That will wipe the device entirely and let you use the device with a new account. As I said before, it will not restore the account. I also think if you try to restore a wiped device with a backup made when it had a now-locked account on it, you will find the device gets locked again. I don't know how many times Apple will reset it for you if you keep on doing that, so I wouldn't even try to start with.
The account is locked, so basically the old account and everything done with it is history except for things kept outside the account. At least the equipment can still be used if you can get Apple to reset it for use as a brand new piece of equipment with a brand new account.
Sorry to hear this happened. Scammers, thieves, abusers and the populace's desire to use devices for things requiring security are forcing tech people to introduce pretty strict measures. Apple has pretty rigid ways of handling this, though I can understand that with millions (if not billions) of accounts it is just easiest to stick to strict methods of handling suspicious account use.
I personally use my account for very little. I only have one purchased app, which I purchased directly from the vendor. Apple has never seen my credit card. I have no balance in my account. The only apps I use on my iPhone are entirely free ones. I only use the 5GB free iCloud which has nothing that isn't already on my external hard drive. So basically if I lost my account it would be a nuisance but not catastrophic.