I have found my answer. I have created a domain. In the hosting panel, I have added a user email account. In webmail, I managed to get connected to that account. I disconnected. In the hosting panel Malibox List, I have pressed then Change password button right to the user email account. The pop-up does not ask me to enter the current password. It just asks for the new password. After changing the password, of course in the webmail I was not able to get connected with the previous one.
As a conclusion: the person who has got access to the hosting panel can change the password of any of the emails in the Mailbox List. In other words, he has access to all the email accounts. Having a user account on mail.serv00.com is definitely not safe in my opinion.