I see your points. I the media has been largely against Trump. But a question raised is whether the media has the authority to determine a claim is a lie. 
Up to now, most media has shied away from that. Trump got five years media access to all but call Obama a Negro born in Africa. I never remember any media saying that is a lie. Trump's recent admission at least means he spread a falsehood - he lied.
Lawrence O'Donnell recently noted the liberal NY Times fell into this trap. Times: ..."in selling his case, Mr. Trump stretched the truth, saying ... Hillary Clinton, has no such plan of her own [for childcare] and “never will.”  But then they wrote ..."Clinton issued her plan more than a year ago...it guarantees up to 12 weeks of paid family and medical leave for a newborn." Stretching the truth or a lie?
Chris Christie recently said Trump has not pushed the birther argument for 5 years, but we have tapes of Trump going to 2011. CNN said this was false. Why can't the media note this?