If, when there are errors on a credit report, consumers were allowed to sue and collect damages rather than having to fight to have the fraudulent entires removed, this would naturally result in a class of "ambulance chaser" attorneys that ran TV commercials and took cases on contingency, but it would benefit consumers as well since errors on a credit report would be more quickly and profitably resolved. The situation would be short-lived, however, as credit reporting agencies would have to make drastic changes in how they verify identities or risk hemorrhaging money from the lawsuits.
But those changes are what needs to happen, so making them liable would be a means to an end.
Furthermore, this only affects the real X, since all impersonators can claim to be Y and get around the sloppy data gathering practices of the agencies.