As an Administrator of a site is there a way I can llop up the information about my site that shows that the Administrator did delete an account of an individual, and what that users name was as well at the time of the deletion, or if that individual themself deleted their own account? The site that I currently administer, this is a brand new site and I am really green here, has a mamber that states their account was deleted by me and I just want to prove to them and to all the other members that this is not the case at all. Is this a possibility at all or am I just out of luck?

It depends on the site and the privledges given the person who is administrating the site.

Administrating a site does not give you automatic privledges afforded the site owner who originally set the site (Xoops or otherwise) up.

So an administrator can say they don't have database privledges and be telling the truth.

I have database privledges on my site because I set it up, so I can look at or read any pm's. No body else can... even if allowed to administrate my site.

Maybe that will help you answer your question.
BS

Sidenote: Yes, the SITE OWNER can, in most cases, if they know how, (and many don't) trace any action preformed on their server.