I'm trying to understand a subtlety here -- The first site says that in order to obtain a B/2 visa, 6 months is required, yet US Citizens are exempted from obtaining a visa.

I understand this is not an Israeli goverment site, but the state department says:
https://www.gov.uk/foreign-travel-ad...y-requirements

"Entering Israel: For non-dual nationals an onward or return ticket and proof of sufficient funds are required for entry. Although the Israeli government does not require that a passport be valid for six months from the date of entry, airlines routinely do so and may decline boarding if a traveler has less than six months' validity on his or her passport. Travelers normally receive a free, three-month tourist visa upon arrival in Israel, which may be extended. Travelers carrying official or diplomatic U.S. passports must obtain visas from an Israeli embassy or consulate prior to arrival."

Furthermore, Israel is listed as a member of the "Six Month Club".

Independent of Israel's regulations, though, I am trying to understand why BA is suggesting that it's a UK immigration policy.