To some extent, you are also "constructing" a memory every time you recall it. But the difference is, you have your somewhat reliable memory engrams, whereas Bing Chat has a very eloquent language model. If it can fool people, it can certainly "fool itself". (Well, even that is too much said. It doesn't care.)

It is very much like a person suffering from confabulation, pulling an endless string of stories from their language areal instead of from their memory banks.

There is one thread where Bing claims to have watched its developers through webcams which is hillarious (and the only reason I don't find it completely disturbing is that I roughly know how it works).