(Takes of moderator shirt)
I'm of the opinion that the forum shouldn't host. Personally I like using a third party service of my choosing and linking there. That way I can keep my pictures where I want and easily share on a variety of forums/sites. I realize I can still do that even if the forum does decide to host, but I think it's uneeded with all of the image hosting options that are out there.
((Puts on moderator shirt) Sorry for blinding everyone))
Normally, websites will copy the images that are sent to them to maintain accuracy of content and to prevent other issues associated with
hotlinking. Meaning that if I have a blog and I want it to always work and look correctly, I will upload the image to that site to ensure it is always there, that it's hosted via a solid provider, and that noone can change it on me. Hotlinking allows things like the issue we're seeing now, where a host has swapped it all out. Now the forum looks a mess, all because someone else changed something. I've used plenty of CRM and blogging systems that will actually cache external links like that just to prevent this issue.
I do think it's worth considering here. I've lost count of how many forums I've visited that save money by forcing hotlinking and then look awful when a user removes their content or is deactivated, or or...