The question is ambiguous.
It all depends on the contract with the user of the resource, and the information itself.
In General it is not - the user posted his problem.
On the other hand there are a lot of nuances - which is spelled out in the contract, whether it is personal information, etc.
One engaged in Internet-resources, a solid Russian company argues that the law requires
If a company collects data about the user specifically, or specially, according to the law the user has the right to request removal of the information. Here, for example, the search engine keeps a history of your requests, etc.
To use search from Yandex user vynujdena to betray him to request some information.
Another thing is when you post a review or blog on a special platform - none of the user specific information is not collected, he published - made public domain information.
And here no one is obliged.
There are some subtleties, but in any case only through the courts, and the court can safely send the user to his wishlist.