History will record marriage laws were changed to include same-sex couples during the 45th Parliament under Prime Minister Malcolm Bligh Turnbull.

But there will be a secondary debate over how much credit the PM should receive.

He was loud and proud amid the rainbow celebrations in the House of Representatives on Thursday night, and it might seem churlish to suggest Mr Turnbull shouldn’t have been centre stage.

However, that secondary political and historical analysis might just question that. And it will underline the point this was the first time he had voted for SSM.

Mr Turnbull is stopping well short of claiming it was all down to him, saying this morning merely: “I’m so proud this has occurred while I’m Prime Minister.”

And there are plenty of reasons for his modesty.

This was a change driven by the Australian people. Parliament acted only after six out of 10 voters in a national ballot gave MPs specific instructions to approve same-sex marriage.

And it was powered by the combined heft of the Labor Opposition and the Greens in the Senate and the House of Representatives.

The Turnbull Government had wanted a full plebiscite, demanded by right-wingers who saw it as a way to impede or destroy the SSM movement. Parliament rejected the idea and the pressure for a direct vote within its walls was renewed.

So the next outsourcing option was a watering down of the plebiscite idea to a voluntary, non-binding postal survey — same intention, different vehicle.

However, the ballot turned on its advocates and $100 million later the Yes vote was a clear winner, and Parliament couldn’t avoid its obligations.

The successful legislation was not the product of the Turnbull Government. It was from a Liberal who sits outside the executive.

The PM supported it, but was just another spear carrier in the free vote.

Further, Liberals including Mr Turnbull had denied the Parliament a free vote on the issue until this year. In 2012, Mr Turnbull bowed to party policy and voted against a private member’s bill in this direction.

That’s one side of the historical post-mortem. Another has a more nuanced view of the Prime Minister’s role.

Malcolm Turnbull at times likes to hint a brilliant chess game is underway, invisible to those without his sophistication and canniness. He is cited as telling colleagues words to the effect of: Just because you can’t see anything happening doesn’t mean it isn’t.

It boils down to how you measure that substantial intangible, leadership. According to his backers, Mr Turnbull had lots of it.

He personally promoted the Yes case during the survey. Remember those twee “Lucy and I …” declarations of ballot intentions? And he didn’t impinge on the No advocacy of colleagues.

The PM joined those who saw the debate as extending beyond same-sex couples getting married. It was a test of Australian tolerance and defence of equality. Further, he gave the discussion a conservative bent by arguing it was a quest to entrench the values of marriage.

He struck a critical balance between leading the debate in one direction while convincing opponents they were getting equal attention. At one stage he appeared to make a tactical retreat by not vigorously contesting the view SSM was a second-rate matter.

It should be remembered he was standing up to the hard-right Coalition rump which had been criticising him on a range of postures for months, while also copping brickbats from moderates for allowing the disruptive, divisive survey.

After the survey, he backed the private member’s bill of Liberal Dean Smith and created a review process which next year will test whether SSM intruded on established liberties.

That was a key counter to the charges that same-sex weddings would somehow trash the freedoms enjoyed by priests and florists.

And there can be no doubting his delight at the bill’s passage.

There is one final measure of the Turnbull factor. Under Tony Abbott and John Howard it wouldn’t have happened. Under Malcolm Turnbull it did.