what does that have to do with the question you asked me?
If you used your real name to register then it would not be a "fake" account. It does appear you have violated the tos by not updating your email address though as required. (Based on their statement about no account registered to the email you used in your Correspondence)
Regardless, they own the marbles. They don't have to let you play with them, even if they let you keep some of them in your marble bag for awhile where you presumed they became yours.
I've been using this email for years. I didn't need to update it. They permanently removed my account, so there's no account left for me to recover with the email I had it registered with.