Yopu need Visa on RTD to visit Israel. I did visit this country on some business trip, their immigration made me to sit for atleast 30 minutes while they spoke with US Consulate to verify/clarify about this RTD. Then they asked me a lot of questions regarding my SSN, my date of first entry into USA etc etc which I beleive that they might have got from US Consulate at that time.
I stayed out there almost for 2-3 months. It is a great country to travel. Almost every street/every corner/every tree is historic. I was stopped by their police once... I am not sure if I was speeding at that time or not.... well! they let me go immediately after seeing my US Government issued RTD.
Just be safe..... keep a safe distance from public vehicles while driving..... Their security agencies are very smart... it's considered that even a sparrow can not fly without their permission..... So overall.... it is a very nice, loving and historic country to visit.