That is indeed what Monash's biographer says, but Monash was Jewish and that didn't make him popular with the Establishment back then. Also, the prime minister and other politicians feared that he might go into politics and beat them, so he didn't have many friends in the government.
Historian Roland Perry, author of ‘Monash: The Outsider Who Won a War’, once put it bluntly: “Bean didn’t like Monash because he was Jewish. Murdoch didn’t care whether he was Jewish, gypsy or geranium; his motive was that he couldn’t manipulate him.”