As far as I can tell, unless you have a copyright assignment from the person who wrote the copyrighted material, there is no reason to think you would have ownership of the copyrighted material. This is why many companies that operate in such a model make you go through a process to become a contributer.
Just e-mailing something to someone doesn't assign them copyright, and I think that sort of thing was decided long ago with mailing manuscripts.
The web interface still is the same. In no case has anyone been able to argue they didn't infringe copyright (of a song etc) based on *the method they received the copyrighted material* - otherwise it would seem to me that bittorrent of a version of a song would not infringe as you didn't have a contract or license appended to the CD (if the CD is old enough)...
Remember, you don't need a copyright notice to get copyright protection now (though you used to, in which case your argument probably would be correct, unless the poster added a copyright notice).
In the case of an ambiguous web interface, I think you need to consider the logic like this:
1) I have received copyrighted content, and no explicit license or assignment.
2) What can I do with this? I personally can view it, but I can't make copies, nor can I distribute it. So I can't put it up on a website I own. This is standard basic copyright law. I don't think anyone disagrees about this.
3) However, my website is providing hosting with the results licensed CC-BY-SA, which is a license that does allow me to share and distribute the copyrighted material. It seems likely that the copyrighted material was posted on my site utilizing that license, especially as much of it is derivative of the existing CC-BY-SA license.
I don't see any way to get to copyright assignment that would hold up in court. I have my doubts that #3 really holds up - the content should be explicitly licensed by the contributor. For it to actually work, it should be, as you say, part of the site contract entered into for edit access - like Slashdot has comments owned by the poster.