One of the Al-Jazeera live feed videos Israel has been sharing is actually of an unrelated missile launch.
I am not clear on if US intelligence has relied on this video. But the Israeli government certainly has at least shared it publicly to argue it was a Palestinian rocket misfiring in air causing the hospital blast. However it is actually likely an Iron Dome missile intercepting an earlier rocket barrage fired from Gaza. This occurs far from the hospital, likely over Israel, and does not cause the hospital blast.
This does not change the Times' (and others) assessment that Israel was unlikely to have caused the hospital blast and that it was likely a Palestinian rocket. It just means some of the videos being shared are of an unrelated event.
"The Times’s finding does not answer what actually did cause the Al-Ahli Arab hospital blast, or who is responsible. The contention by Israeli and American intelligence agencies that a failed Palestinian rocket launch is to blame remains plausible. But the Times analysis does cast doubt on one of the most-publicized pieces of evidence that Israeli officials have used to make their case and complicates the straightforward narrative they have put forth."