The notification that you saw is not useful legal information for you: stuff always belongs to whoever owns the stuff. It might be interpreted as saying "it doesn't belong to us", but you can't count on that (it's virtually guaranteed that at least some of the content there is owned by the website owner). A more informative statement would be "You will have to get permission from the content owner to copy their stuff", and "We're not going to spend time figuring out who owns what".
You could read the terms of service (try this with Stack Exchange) to see what the site tells people. The TOS here says that if you contribute anything, it "is perpetually and irrevocably licensed to Stack Exchange under the Creative Commons Attribution Share Alike license". You can then look up what that license says and learn what that allows. Websites are kind of tricky, though, because it's not hard to change the wording of a TOS, and you need to know what specific TOS was promulgated at the time a particular contribution was unleashed. Usual practice is to think it through carefully and not frequently tweak the TOS, but it's not illegal to change the TOS. Note that copyright law does not prohibit you from using other people's stuff, it prohibits you from copying. The distinction is clearer when you see a post that explains an algorithm with actual code, you read and learn and make use of that, but write your own code. As a user out there, if there isn't a clear indication that stuff posted is there for the taking, under some public license (as is the case with SE), then getting specific permission to copy, from the owner of the content (possibly untraceable), would be necessary.
Now assume that you're a moderator or site-owner of some forum: presumably (hopefully) you have a TOS that addresses that situation, which says that moderators have the right to edit or delete content at their sole discretion, and also you say what kinds of posts are prohibited. Such an statement is not absolutely mandatory for all things, but it may be necessary to avoid litigation over some acts. One one end of the spectrum, it would be illegal for a forum to host child porn, stolen credit card numbers, or protected digital content. If a user were to post such stuff, the site would need to eliminate that stuff, and the poster could not legally rely on an argument of the type "That's my stuff, you have no right to mess with it".
On the other hand, if a forum actually requires paid membership, then there may be a strong contractual expectation that the user is getting something of value, so you would have to watch for statements that could be interpreted as broad permission to put stuff out there without any interference. (For instance, a file-hosting service would have only minimal restrictions on content, aimed at protecting their own legal interests; whereas a political-advocacy site would have maximal interest in prohibiting the expression of views counter to the cause). Thus the SE TOS has you "grant Stack Exchange the perpetual and irrevocable right and license to use, copy, cache, publish, display, distribute, modify, create derivative works", which allows moderators to correct typos, delete offensive wording, and obliterate entire posts. If a site fails to have any such clauses in their TOS, then it might be a matter that has to be settled in court, whether they have the right to eliminate "spam" (i.e. advertising for a service, especially if the reason for getting an account was to provide an advertising platform).
In light of the limited use sanctioned by the TOS, per the below comment, legal copying will be quite limited. However, "fair use" a situation where copying is allowed, regardless of what the TOS may say. (You could be banned from the site, but you could not be sued for infringement). Fair use was invented precisely so that people could make comments like "Jones advocates an absurd law, saying '...[quote from Jones]...'". Thus you can comment on a post and quote the relevant part ("The lines '[... quoting the code ...]' results in an infinite loop"). See the Fair Use FAQ for more details.