
I have likes and dislikes for each side, but ultimately I'd suggest allowing "guest" posts.
On one hand allowing guest posting can sometimes be a problem for both the forum and user. The forum can sometimes get random, 1-shot posts or posts that are down right false. For the user, if they make a mistake and want to edit the post they can't. It also screws up any type of flow if the same person posts a follow up.
On the other hand, a casual user that happens by the forum might have something of value to add, but doesn't because they don't want to register for yet another account/password. I know I've had this experience before. I've wandered into a forum and wanted to add a post, but didn't because they didn't allow guest posts. It wasn't a forum I would actively ready so I didn't want to go though the trouble of registering for yet another account.

A forum is kind of like a moderated newsgroup. A newsgroup has no restrictions on postings.
Personally, from the admin side I would prefer not to allow guest posts. From the user side I'd prefer to have it. I think the user side should prevail when possible.
In the end, I think allowing more people to post that otherwise wouldn't is a good thing. It's not like the forum is being flooded with nonsense. Why not continue to allow guest posts and revisit the issue if it ever becomes a real problem.