No. An OR statement does not imply that it is all at once. That is an AND statement.
In fact, in speech and writing, an OR statement is also often exclusive; i.e., it implies that it is not two or more of the terms at once. This isn't the case here, but your conclusion is still fallacious.
In fact you're clueless. I can use ANY of the following: friend, associate, business partner.
What is your native language?
If I define a wubble to be a bubble or a flubble, I cannot assume that a wubble is a bubble and a flubble. I also cannot assume that a wubble is a bubble, nor can I assume that a wubble is a flubble. This is the magic of OR.
You cannot just simply use ANY of the options you listed; there is uncertainly as to which one it is. It is therefore impossible to prove that "friend" is correct from the given definition.
Your logic is keep failing you. If there is
then I can use any, especially if I believe that it was an imaginary friend.