As I understand it (and if I understand your question correctly) Israel does indeed require transit visas.

Has he already tried to get a visa?

any idea how people from the gulf area visit Israel thru Jordan by bus without an Israel stamp?

Israel will, on request, stamp a piece of paper instead of your passport. The problem is that you can still get busted for an neighbor's exit stamp, but I seem to vaguely recall that you can get around this in Jordan if you use the Allenby Bridge (to West Bank, not Israel proper).