I'm not 100% sure on this but you need to check out what rights users may have to delete the own posts. It is my understanding that EU citizens have that right although most forum owners will not allow further participation in the forum after posts have been deleted as it is so disruptive to forums.
On my forum, based in the EU, the topic was raised and this is how it was dealt with by the Admin. Nobody's rights were infringed and following the common sense explanation below nobody else has raised the topic since.
Admin wrote:If you engage in a conversation with another person you cannot simply erase a statement or change a statement that you have already made. You can expand on the statement or qualify the context in which it was made but you cannot un-say what has already been said. Likewise if we were to have an exchange via text messages would you expect to be able to erase or edit messages to which I had already read and responded? You could change the whole nature of the original conversation to make it look like a completely different conversation. What if the person you were texting could do the same? You could be made look like a fool or a liar based on your responses to their deleted or changed texts.
When you make a post you put it out there for the whole world to read and react to. Nobody made you post it, you chose to do so of your own free will. You have to stand over what you have said, just like real life.
Naturally we will allow exceptions to cover say inadvertent disclosure of private information or personal details but other than that be mindful of the fact that, in forums like in real life, what you say cannot be unsaid.