I'd go one step further. Instead of simply quoting people, the Times should investigate the story and report on the facts. If the Dems called for X and some Dem said Y, it needn't immediately go to press. How about verifying the veracity of the statements first. Then, publish. Finally, if an honest mistake was made, formally retract the incorrect statement and be transparent about what and why an edit to the original story was made.
There is a story here. Sessions was questioned during his confirmation hearing. He was asked a question. He answered the question. Did the revelation of events alter the truthfulness of his response? The Times does not need to simply act as the DNC propaganda wing by repeating Democrat's demands. They are irrelevant and are not newsworthy. Who cares if Pelosi is calling for Sessions to resign or recuse himself. Either he lied and should be tried for perjury or he didn't. As it is being reported, it is just a series of sensational demands made by politicians for political gains without any firm basis of reason or fact. The Times is offering itself as nothing more than a DNC advertising flyer.
On a more philosophical note, is a corporation that works with/for a political party still considered a member of the press? Are organizations like Fox News, MSNBC, the Times, HuffPo, et al truly members of the press if their prime motivation, outside of making money, is to carry the water of a political party or interest? Maybe, we need to re-examine how we define the press in the first place.