No they wouldn't. The libellous Barcelona stories this year alone should tell us that. People very rarely bother to sue about stuff like this, and when they do, the papers can easily afford to pay the lawyers' fees, and the compensation if they lose, so it's worthwhile for them anyway. Even rich people are always denying stories but not bothering to take it to court. It would be easy in cases like this one, if it's false and Rooney were to deny it and try to sue, for every publication who got the story from the Mirror to say they were just trusting the Mirror, and for the Mirror to say they checked the prostitute out, decided she was reliable and only reported what she told them (it would also be easy for them to say there is unfortunately no audio evidence of what she actually said to them). Proving that a publication deliberately printed a false story is often very difficult, and often it's more of a case of them eagerly printing what they're told than of deliberate fabrication, which is harder to sue for.
Rant made me feel better. So not pointless.