Your faith in Israel is remarkable

. That's something at actually seems quite possible. As for Mubarak, are you saying that he'd be assassinated by an Israeli sniper once more?
No, I meant that Mubarak might be the victim of the same kind of internal Egyptian plot as Sadat was OTL, if he took part in an analogue to the Camp David agreement.
I'm sorry but the real world doesn't work like that, conspiracies like that rarely are even thought of in the moment (most people just don't think like that) and they NEVER work, there are no men on the grassy knoll ok?
TBH, there's not a huge conspiracy beyond "tell the sniper team in question to shut up and then produce press releases that say... well, they say what is best for everyone." Well, ok, maybe there is a little bit of one in that they need to find somebody to play the part of a dead assassin, but that can't be too hard.
Very few people will know what actually happened.
Lots of other people will deliberately lie about what happened, regardless of what actually happened, and what anybody else is saying about it.
Not a chance in hell. The Israeli government - and especially the Israeli army - would never do something like that. If the sniper in question could make a good case for himself that he thought Sadat was a terrorist (and that he hasn't just wanted to assassinate Sadat), he could probably even come out of the whole thing with a pretty small punishment.
Sorry, I was unclear. I certainly don't mean that the Israeli army would shoot their own sniper! In the heat of the moment, though... Would Sadat have a bodyguard? Would they return fire? Would he be treated in Israel, or would the plane try to take off again immediately to return him to Egypt?
Certainly all the witnesses will be unsure of what happened, and Israeli security will immediately (as at the time they won't be sure what's happening either) try to move all the witnesses away from the plane and under cover. The majority of cameras will be watching Sadat, and hopefully none will be in position to see both shooter and victim.
It's in that atmosphere of immediate confusion followed by an initial press blackout (legitimately driven by the need to safeguard everybody present from further shootings) that the choice of what story to present faces Begin.
I think Israel would just keep everything secret enough, for long enough, to muddy the waters enough, to let other governments, which in all honesty would rather the whole thing just go away, have political cover to not get involved, particularly if groups on the Palestinian side begin to stick their own oars in.
Of course the truth will out sometime - but equally so will many many conflicting lies, and in all the confusion there might not be yet another Israeli-Egyptian War (which Israel would win, but really, is it worthwhile to fight one because some schmuck couldn't tell the difference between a deadly commando assassin and an old balding man in a suit)?
I really see any claim of "
yeah, we shot the guy who launched that invasion across the Canal, but it was totally an accident!" as going over like the proverbial lead zeppelin - why would anyone believe it was anything other than a deliberate execution by a vengeful Begin, with a total non-apology which basically translates to "OUR WORDS ARE BACKED WITH NUCLEAR WEAPONS," as they used to say in Civilization.
Instead, surely it's got to be Big Lie time, first because too many people will not believe the truth, and second because the consequences of that wrong belief are too difficult to predict and high-impact enough to risk a cover-up. There's too much danger that honesty snowballs into a second Zimmerman telegram and turns the Carter administration against at least the Begin administration.
On another note, even though we on AH start with the premise that the shooting is an accident, will the Israeli authorites believe that story? Did the shooter lose friends or family in '73? Somewhere in the chain between rifleman and Prime Minister, might not someone decide that it was an incident, not an accident? Would that affect the calculus of how to spin the story?