Staying on the topic at hand, and only that, this is war. Killing an enemy on the field has no system of public review. Everything is internal. Neither IDF or Hammas has to provide proof of anything to anybody for any reason except when propagandantistic PR is at play (like you mentioned). At least not now. There will surely be tribunals after this war is "settled." The only direction proof goes is up the chain of command. I won't pretend to understand the complexity of target selection and acquisition (especially foreign nations and certainly not terrorists), but I know that that's how it works. There is no burden of proof, whatsoever.
Those are the cold facts.
Opinion, etc: I hope you don't read this as some kind of defence or exoneration of any malicious, evil, callous, or accidental killing commited of innocents. I unequivocally do not want or excuse killing civilians. Anyone who does is hideously evil. However, I think a reality check is necessary.
The "burden of proof" is a security blanket most of the world enjoys and vaguely understands. When they see some horrible violence of war, fed to them without context by compromised sources, it's easy to make assumptions and demand justice. And many of those times, you should, just ideally without the assumptions and propaganda. This isn't one of this times. I know that the IDF is commiting war crimes, but this video is just war.