Have you considered that things might go the other way around: if Russia had such a strong influence on the US through its political action lobby as Israel does, Russia would be considered by politicians the main ally of the US, and the economic and military ties between the two countries would be unbreakable. Because the purpose of these lobbies is exactly to influence how a certain country feels and acts about another.
No. The US would be convinced it got another valuable ally- which is not the same as actually having one.
In pretty much the same way, those who fall for long distance romance scams didn't find the love of their life, despite believing so. They found someone who is taking advantage of them.
