My iamnotalawyer understanding is that, yes, user X could remove the original attribution on the non-Stack Exchange site.
When an author creates any work in the first place, the act of posting it on SE grants a license to that work under CC BY-SA 3.0. The original author still can choose to use that work elsewhere and issue a different license to that same work as generally, their copyright or other moral rights are still reserved. (With the disclaimer that each locality has different interpretations of what a work for hire and what creations can even be protected by licenses.)
In almost all societies, Licensing a work under the SE/CC terms doesn't necessarily change an author's ability to reuse/relicense subsequent uses of that work - including copyright enforcement if the terms of the CC license are violated.
The original creator could still take their work and use it in some other way. For example, they may have applied a no-commercial CC licence to the work, but they could still separately sell that work to another party. They could choose to allow that third party to sell it on.
More concretely, you could publish Flickr photos with non-commercial licences, but still sell a photo to a newspaper, or offer it to a photo agency to sell on to newspapers and so on.