Another advantage to "threaded" mode is that it shows you the messages ordered arranged by reply rather than just by "last posted"... IOW it shows you each message in the "thread" linked to the post that it is replying to. This makes it easier to follow all of the "branches" of the conversation in a long thread. "Flat" just shows them all laid out in one string, in the order (by date and time) posted, without regard to which message was a reply to which particular other message.

Of course this only works properly if people use the proper "reply" button when they post a message. I try always to use the "reply" button for the specific message I am responding to in order to keep the messages linked up properly.

So say for example someone starts a new topic with a question. Other people reply, but during the reply some other related questions come up. People continue answering the original question but others are answering the secondary questions. Reading in "flat" mode, you may read an answer but not know which question it is an answer to, which may render that answer meaningless. Switching to "threaded" mode you can see the answer and which message held the question that it answers.

As to the "Who's Online" page... I think the forum software might treat a page open in "threaded" mode as a different type of event as a page open in "flat" mode. Why it should report them differently may simply be what Topher said, "because it can be." It might be of some use to an administrator working on the software, wanting to know which posts in the database are open or something, but I can't even really think of a specific reason why that would be necessary either (unless you just wanted to see how many people use flat mode vs. threaded) so we're back to "because it can"