Yes, but the claim that they're the US's dog on a leash is not entirely true. They have consistently operated in their own interests and against the US's interests many, many times. The US depleted their anti-air missile stockpiles during the 10-day war with Iran.
Entrapping pedophile politicians and bugging the president don't seem like something a loyal dog would do. If Britain, France, or Germany acted in the ways that "israel" did they would be invaded.