There have been lawsuits against MSM. It is high bar to meet but do you want a low one ?
But please remember that the truth is a absolute defense against slander and libel.
Actually, you are a bit mistaken. If a private person sues a media outlet for defamation, the burden of proof is much lower. In some states, only negligence needs to be proved if a private perso sues a media organization, as the NYT found out in the Atlantic Olympics bombing incident.