Bowen is right. It is black and white, a Commonwealth responsibility.And if you read the story you have linked, you will find that the responsibility was referred to the states by mutual agreement.
If you read the Constitution you will find it is black and white, constitutional powers can be referred to the other tier of government when necessary to do so.
I've read the article, and (some of) the constitution. Whatever his other failings may be, Bowen is right: it's black and white, Quarantine is a Commonwealth power. It's not by mutual agreement, it's in the constitution.
The mutual "agreement" is the Feds have effectively said "if you don't like it, do it yourself." The States are using their health powers to implement their own supplementary quarantine, in response to the inadequacy of those provided by the Feds (ie virtually none).
I don't know if it's a left/right, or competent/incompetent issue (Trump vs Reagen?), but I think a fair comparison with overseas countries and their response and it's effectiveness are NZ and the UK. Our Feds have taken a position not unlike the UK gvts. Our states more like NZ. As a consequence we are somewhere in between - but closer to NZ because we *have* a (more or less) functioning quarantine service - operated by the states rather than the Feds as the drafters of our constitution envisaged.
Bowen is just trying to big note himself and while he maybe technically correct regarding one aspect of the constitution, as I posted in April its not so simple.
As others have said its a long-term convention agreement between the states and feds who looks after Health and quarantine and it is 100% the states. The NSW govt has confirmed this to be fact when it admitted fault over the Ruby Princess. The Fed's also have almost no resources to do so which is an outcome of a 120 year long agreement.
So you reference to "The States are using their health powers to implement their own supplementary quarantine, in response to the inadequacy of those provided by the Feds"
is actually rubbish.
If you would care to educate yourself more on the numerous "mutual agreements" that are in place, you might be surprised. For example Abbott tried to pull out of what was becoming a longterm acceptance that most suburban rail projects receive Fed funding stating that Suburban rail is the states responsibility. He was 100% correct, but not a popular statement.
If I'm correct, the states have also given the Feds the power to levy income tax by "mutual agreement", a move they did to fund I believe WW1 (open to correction), but this has never been formalised as permanent. Likewise the Fed's levy state excise tax on fuel and hand it over to the states by "mutual agreement". All because some lawyer realised that what the states were doing was illegal under the Constitution, it was all fixed literally over night due to the need to not interrupt the states income stream.
The Fed politicians' used to have a "mutual agreement" on how they all saw Section 44, until someone big noted themselves.
As with many other aspects of Australian and state govt, yes, our effectual duel govt level causes issues when compared to NZ, where the NZ PM doesn't even have a upper house to deal with. The UK is not alot different, although they have other problems in their governance as we saw in BREXIT where to many people thought that the Q to leave the EU was actually a legally enforceable referendum when it was legally nothing more than a survey due to the lack of a UK Constitution. Then they appealed to the Queen, who hasn't counteracted the PM in over 300 years.
So rather than compare "blindly" Australia to countries with only one level of govt (excluding local), you need to compare more with US and Canada.
Final note, I have stated in various forums here for years Australia need to move away from this dual level governance to simply make it easy to get things done and be very clear on accountability to voters. Note just quarantine, but health, PT, Education, Road infrastructure etc etc etc. The formation of the ARTC was in part a move towards Fed ownership of the interstate network.