AFL boss Gillon McLachlan used high-level access to Liberal Party ministers to ask about visas for an Argentinian polo player as well as a French au pair, a Senate inquiry has heard.

Wednesday’s committee hearing was meant to focus on a visa granted by immigration minister Peter Dutton to a French live-in nanny after representations by Mr McLachlan, but was briefly deviated by the curious case of a male Argentinian polo player who was a “friend of a friend” of the AFL executive.

In 2014, Mr McLachlan told the AFL’s head of government relations, Jude Donnelly – herself a former Liberal Party staffer – to find out “whether the visa had been approved or not” for this polo player.

Ms Donnelly then contacted a former colleague at the prime minister’s office.

“Which prime minister at the time? There’s been a few,” Labor’s Senator Murray Watt joked.

Tony Abbott, was the reply.

“I believe this guy’s waiting on a business visa. Could you let me know the status of where it’s at?” was the rough wording she used, Ms Donnelly said.

She heard back “within a couple of days” that the polo player’s visa had been granted.

It was an insight into the level of access on visa matters afforded to prominent public figures by Liberal ministers – access denied to others.

The inquiry heard from three migration agents who said they had never obtained ministerial intervention over the phone, and never without substantial documentary evidence. They said their requests for ministerial help was usually denied, despite weeks of work.

The AFL’s Mr McLachlan was asked why his second cousin, Callum MacLachlan, had approached him for help in another matter – the now infamous case of a French au pair detained at Adelaide airport in June 2015 on suspicion of intending to work illegally.

Mr McLachlan said his relative called “agitated and concerned” on a Sunday morning, saying there had been “an error”.

Why did the cousin approach him for help, the AFL boss was asked.

“I imagine he had an instinct that I would have a level of some contact that would help him get in touch with [Peter Dutton’s] office,” Mr McLachlan replied.

After “probably two” phone calls and “a couple” of emails by Mr McLachlan’s staffer – again, former Liberal staffer Ms Donnelly – the French au pair was freed and granted a visa.

What documentation was attached to the email?

“I forwarded the email from Gillon’s cousin Callum and just the factual information around the passport details,” Ms Donnelly replied.

In contrast, migration agents had spoken of needing to supply volumes of supporting documents.

And did the French woman ended up working – illegally – as an au pair for Mr McLachlan’s relatives?

“That’s not my understanding, no,” the AFL’s Mr McLachlan replied.

It was one of only 14 times Mr Dutton had intervened personally in tourist visa decisions in his four years in the immigration portfolio, the inquiry heard.

It was an at times fiery hearing, with Coalition senators Eric Abetz and Barry O’Sullivan clashing with the Labor chair, Louise Pratt.

Senator O’Sullivan interjected repeatedly, and at one point told Senator Pratt that she was “not chairing this correctly”.

Senator Pratt forced him to “withdraw his reflection on the chair”.

When Senator Pratt accidentally referred to him as “Senator Sullivan”, he slapped the desk and said her memory was “a bit frail”.

Labor’s Senator Watt sniped: “I think if any of us were under any misunderstanding that Minister Dutton was in trouble, the fact that it’s Senator Abetz and O’Sullivan who showed up today just confirms it.”