The press needs a better game plan than "Here's what the terrorists say happened."
What the MSM and other mainstream liberals were desperately looking for was a way to balance out the moral scales (in their minds).
After Hamas committed their barbarian rape and pillage campaign liberals were placed in a very uncomfortable position: it was obvious to everyone either not on the academic Left (or not terrified of the academic Left) that this was a moral outrage that any person who claims to be dedicated to "Justice" etc would obviously need to vehemently denounce. But denouncing Hamas in "Left spaces" codes as punching down, putting yourself on the wrong side of the Oppressor/Oppressed binary (the only acceptable worldview among the liberal class), and liberals were terrified (as they always are) of a horde of shrieking internet Furies denouncing them as white-supremacist bigots.
Thus the hospital rocket was a gift too good for them to pass up (or fact check): now they could avoid taking a stand that might damage their personal and/or professional lives (and brands) and go back to making bland speeches about "atrocities on both sides".
No matter what the issue and no matter how much they talk about Justice and Progress, the liberal gentry class always considers their social and professional needs first and foremost, and being forced to take the side of Israel here has made them very uncomfortable and searching for a way out.
Is it possible to get accurate figures for Gazan deaths? Hamas not only lied about the source at the hospital, they liked about the impact. Is there any way that we can get a record of deaths in buildings where the Israelis notified the occupants to vacate vs those killed on the street from falling rumble, killed by Hamas for not cooperating etc.