The full text of your article explains what it means by the US "meddling":
For weeks, President Donald Trump and Secretary of State Mike Pompeo
have been claiming without evidence that the Covid-19 pandemic is
linked to a lab in Wuhan that researches bat coronaviruses. Their
efforts are clearly calculated to distract from Trump’s bungled
response to the virus, and, for rational observers, they have tainted
the notion that the outbreak began with a lab accident or safety
breach.
[...]
“An open investigation is absolutely warranted and absolutely
essential,” said Richard Ebright, a professor of chemical biology at
Rutgers University. A longtime biosafety proponent, Ebright believes
that a lab error is “at least as probable” as an entirely natural
spillover event. “Unsupported claims by Trump and Pompeo have
politicized and polarized the issue and likely have had the effect of
making an open investigation less likely.”
This is expanded upon a little by the Guardian. The Morrison government's original position was to gather international support for an "independent review at the right time", notably one that would look at the virus' origins:
The review would look at the outbreak’s emergence, development into a
pandemic, the WHO’s and broader international response, and ways to
strengthen the world’s collective ability to respond to pandemics.
The Australian government wants the changes to include strengthened
inspection powers for the WHO. At the World Health Assembly on 18 May,
Australia plans to support an EU-sponsored draft resolution that
includes a call for an independent evaluation to review lessons
learned.
However, the US release of a dossier which it claims gives weight to the theory that the virus originated in a Wuhan lab, and in particular, the implication by the media that this was prepared as a result of intelligence by the Five Eyes alliance - something which is denied by Australia - gave weight to claims that Australia's intention was to politicise the issue:
Allan Behm, the head of the international and security affairs program
at the Australia Institute and a former senior defence official, said
those pushing the Wuhan labs story without solid supporting
intelligence or evidence were not helping Australia’s call for a
properly conducted international review.
“It just doesn’t help Australia in pushing that, any more than fake
intelligence on WMD helped the credibility of John Howard in 2003, and
I suspect that’s why the government is treading very carefully this
time,” Behm said.
These fears were proved to be well-founded, as China ramped up criticism of the proposals, eventually settling for the EU-drafted proposal which notably does not include a review of the origins of the virus. Indeed, a Chinese state media report published after the adoption of the EU proposal characterises the Australian-backed review's intention to include an investigation into the origins of the virus as "specially targeting [a] country based on a presumption of guilt".
So the issue is that Australia wanted to present their calls for an international investigation, which would include a review of the origins of the virus, as open and unbiased. The article's argument is that the US dossier release allowed China to present this position as politically biased from the outset, especially as Australia is a member of Five Eyes. Indeed, Chinese state media called Australia a "US pawn". This, the article argues, led to the scrapping of the part of the investigation which would look at the origins of the virus, as the final language signed up to by China now only calls for a "a stepwise process of impartial, independent and comprehensive evaluation […] to review experience gained and lessons learned from the WHO-coordinated international health response to COVID-19, including the effectiveness of the mechanisms at WHO's disposal."
Whether this was an intentional act of sabotage by the US seems very unlikely - I'm certainly not aware of any claims that this was an intentional move to weaken the WHA's resolution - the article makes the argument that this was just an exceptionally ill-timed release of a document which it claims was "calculated to distract from Trump’s bungled response to the virus".
