It's right up there with "the pub test", "I'm not going to engage in hypotheticals" and "the only poll that matters is on election day" when it comes to big yawny cliches.

Whenever a problem flashes so much as an ankle, the call inevitably goes out for an investigation. Which means that when a genuinely worthy issue comes along, it's like the boy who cried inquiry.

The Greens want two inquiries – one for each house of federal parliament – to check that MPs have citizenship only to Australia. They argue that independent experts, in subjects such as the constitution and immigration law, should be hired to assess MPs' claims. If doubts still linger at the end of this, individuals can be referred to the High Court.

The beauty of the proposal, they say, is MPs will be compelled by their respective houses to provide evidence. And it can piggyback off the existing committee system.

But for this to go anywhere, support is needed from either the Coalition or Labor. And right now, there would be more support at a publican convention for Dry July than there is for a citizenship audit among the major parties.

Which is a problem. Because we need to confirm that the people sitting in Parliament are entitled to sit in Parliament. And as an extension of this, that the government is entitled to be the government. As inquiry topics go, they don't get much bigger or more serious than this.

It is easy to dismiss the citizenship inquiry idea as an attention-seeking exercise from the Greens – something to distract from the fact that they've already lost two senators in this citizenship snafu. But it's not good enough to take the parties' words (uttered on the record and furiously on background) that they have good vetting processes in place. With two senators having resigned, one cabinet minister gone and genuine question marks over others within Parliament, this is a special situation.

We can't leave it up to the media, either. For one, other issues – terror raids, same-sex marriage – have already pushed it off the agenda, even though it is not resolved. For another, journalists can't compel MPs to provide proof (take it from someone who has done two ring-arounds to MPs since the citizenship situation presented itself).

Look at overseas-born MPs, for which there is a definitive, Parliament House-issued list to work through. Of the list of 23, only nine or 10 (depending on your definition) were able to provide Fairfax Media with some form of documentary evidence to prove their citizenship status. This ranged from letters from the British government confirming citizenship had been renounced (a la Tony Abbott), to a photo of an envelope showing renunciation forms were sent to the Egyptian consulate by a certain date (Anne Aly).

Others argued they didn't need to provide documentation. Finance Minister Mathias Cormann says when he became an Australian citizen, he ceased to be Belgian. Others say they have documentation but will provide it only to parliamentary authorities. Others again just insist they meet the rules.

So this is far from conclusive. And this is the easy group – the known unknowns.

Where it gets really tricky is in the group where citizenship can be conferred through descent. This is a mess. There is no master list, so it relies on individually researching MPs' backgrounds (sometimes back multiple generations) and determining whether they have heritage (such as, Italian, Irish, Greek) where citizenship happens automatically or can be acquired.

It relies on identifying possible problem scenarios and asking MPs whether they ever took up dual citizenship or actively renounced it. For some, such as Greens leader Richard Di Natale, it has been easy to provide proof (he got a certificate from the Italian consulate). For others, the situation is less straightforward. Australian-born Liberal MP Julia Banks may have acquired Greek citizenship automatically through her father. Banks says she has never taken up dual citizenship, but legal experts have been unsure about whether she needed to take active steps to renounce the Greek component, nonetheless.

All this requires an in-depth knowledge of multiple countries' citizenship laws, which is not at the disposal of the media surfing the 24/7 news churn. Sometimes you have to call in the experts.

It's extremely weird that our adult MPs don't seem to be on top of their citizenship status. And the constitution is not in sync with today's highly multicultural society. But that's the situation we're in.

Of course, the numbers simply aren't there in Parliament to hold an inquiry (the government does not want to lose an MP in the lower house, Labor doesn't want the scrutiny). From a political survival perspective, this is understandable. But for the rest of us, it is a disgrace.

Because we can't be 100 per cent certain that the people we elected – and pay – to sit in Parliament are actually eligible to be there.