I disagree: almost all CEOs, presidents, Presidents, and leaders of organizations rely upon their subordinates to vet, analyze, and substantiate claims, even as they become spokespeople for them. Even had Foxman seen the work, there would be no reason for him to address whether it's an anti-Semitic work, because the organization is claiming that something more specific in the opera could lead to violence. He also has a Board with its own opinions and interests.
I don't think Gelb would have pulled this had there not been pressure from his bosses. He's not stupid or uninformed about the controversy over the opera since it premiered in 1991. I suspect the Met was ready to capitalize on it, and it would have been a great tie-in to other organizations and presentations about Middle Eastern politics and by academics and many other opportunities to grab that elusive "new audience" that won't be drawn in by the Zefferelli "La Boheme."
Where he was caught flatfooted was is not anticipating that he'd be pressed to backtrack. He couldn't have anticipated the recent killings at a Kansas City synagogue, making the Kansas City-based AMC Theaters willing to play hardball. (Were he to go forward with alternate theaters, the Met in HD that he worked so hard to build might collapse.)
There are a lot of cumulative financial and labor-related reasons for the Met Board to be ready to scapegoat him over "Death of Klinghoffer," including a likely labor action. I don't think the Met will collapse and close, but I do think there's a good chance, based on current posturing, that this could take a while to resolve, and that December holiday/tourist season will be a target for the negotiations.
There's no more NYCO: maybe people will go to NYCB's and ABT's fall seasons instead.