What association to the forum does the member objecting to the link have?
Because, as far as Im concerned its up to the website owner to dictate what is ok and what isnt, usually
by setting out some rules.
Posting a link in your signature isn't "stealing advertising space", especially if the site isn't being moderated - as theirs no one to contact regarding advertising, or anyone to object and remove it.
Also, if the person with the link is an established regular member of the forum in question then its perfectly reasonable for him to link to his own website. if hes just signed up and is spamming his link then thats obviously bad.
But from the sounds of it, it doesnt seem like much of a problem and I cant see why this other member is so against someone linking to their own site.
But as I said at the start, it would be up to the site owner to decide what is ok and what isnt, if s/he doesnt care, then theres not much that can be done really.