Makes sense! Turnbull “pleased him [Greene] that he could humiliate the son of the great Vito Corleone in public” and did

Greene thought the Corleones were washed up Hence Greene could slap a Corleone around in public, insult another Corleone and still keep the Hotel

Don't mean to be pedantic!
What confuses me - the way Greene breezed in with a swagger, full of “confidence and disdain of the Corleones” “hey Mike, hello fellas” and offering “everything you want” - was “Moe scared? behind all that bluster”

Michael undoubtedly goaded Greene and succeeded ["murderous rages"] with his “Corleone Family wants to buy you out”
Greene promptly loses his temper and reveals “I talked to Barzini I can make a deal with him and still keep my hotel

It seems to me whilst Greene figured Michael's visit was an attempt to collect on the IOU [though Greene seemed to think indignantly his 'favour' of taking Fredo in, when the Corleones were having a bad time, squares the deal and he owes nothing] Greene seemed confident he was prepared and invulnerable with Barzini 'guarding' Greene and his hotel

Greene was slipping! Someone was able to just walk into the massage room and “put a bullet through his eye” unless the masseur was the same guy as Sonny's Causeway toll-collector!