Malcolm Turnbull’s implied criticism on Sunday of Tony Abbott’s policy on asylum seekers was not surprising. It’s unclear what role Turnbull will play now he has decided to remain in federal politics, but quite a few Liberal leaders have made a post-political career out of publicly criticising the party they once led.

The list includes John Gorton, Malcolm Fraser and John Hewson. On the Labor side, Mark Latham is the only recent former leader to become a constant and embittered critic of the ALP.

Laura Tingle’s revelation last week that Fraser had severed ties with the Liberal Party received more media attention than it deserved. In Malcolm Fraser: The Political Memoirs, which Fraser co-authored with the journalist Margaret Simons, a clear hint is given the principal author did not vote Liberal in the 2001, 2004 and 2007 elections.

On the ABC2 News Breakfast program, Simons expressed surprise that no one had asked the former prime minister whether he was still a Liberal Party member when his book was released earlier in the year. Perhaps this is best explained by the fact that, in his memoirs, Fraser declared he had “decided to stay” in the party. Now we learn he handed back his honorary life membership in early December – well before his memoirs were published.

Fraser’s memoirs contain a disturbing number of errors of commission and omission. According to the book, by 1990 Bob “Hawke had now won four elections – the same number as Fraser”. Since the Second World War, only three prime ministers have won four or more elections. Namely, Robert Menzies, Hawke and John Howard.

Elsewhere in his memoirs, Fraser maintains that, as prime minister, he retained Gough Whitlam’s Medibank system. Not so. Fraser came to office in 1975 and Medibank had been abandoned by 1981. Hawke created the current system after he was elected in 1983 and it was continued by Howard.

What’s important about Fraser’s present stance is not his personal hostility to Howard but rather his attempt to define what should be the core of Liberal Party philosophy. Fraser claims he is in the tradition of its founder Menzies, which he defines as liberal while the likes of Howard and Tony Abbott are not. To Fraser, Howard and Abbott are conservatives.

Liberal backbencher Petro Georgiou joined last week’s chorus depicting Menzies as a liberal rather than a conservative. During his first stint as prime minister, during the early war years, Menzies outlawed the Communist Party and some of its members went to jail. Soon after Menzies returned as prime minister in December 1949, he unsuccessfully attempted to ban the Communist Party.

Menzies committed the Australian Defence Force to military engagements during the Korean War, the Malayan Emergency, Vietnam and the Indonesia-Malaysia Confrontation. In 1964 Menzies announced the introduction of conscription for overseas military service. In the 1960s, he introduced tough national security provisions into the Crimes Act. These were not the actions of a small l liberal. Fraser was a Liberal MP at the time when most of these decisions were made.

Last week, Fraser told Tingle the Liberal Party’s present advertisement depicting asylum seekers descending on Australia reminded him of the “red menace” advertisements of the late 1950s and 1960s. Fraser claimed this advertisement was “a throwback to a racist past, and not just for the Liberal Party but for Australia”.

This comment overlooked the fact Menzies was the Liberal leader when China was depicted as a threat. Moreover, there was nothing “racist” about the concern held by Menzies and others at the time (including Fraser) about China. In the 1950s and 1960s the Coalition committed the ADF to fight alongside Asians (Koreans, Malays and Vietnamese) against other Asians (who were aligned with communist forces).

In The Sun-Herald at the weekend, Peter FitzSimons related how, at the Byron Bay Writers Festival some years ago, Fraser was “warmly and very loudly applauded” for his criticisms of Howard by a “crowd of literary lefties … who all once eviscerated him as the embodiment of all that was evil”.

That is a reminder Fraser gets a run these days primarily because he has become a hero of the left. That’s all very well. But it is not the Liberal Party constituency – not now and not in Menzies’ day.