No, that is one of the bits that is true. People arriving in Australia from overseas - including Australian citizens - were required to spend time in hotel quarantine. But it was their choice as to whether they entered the country - they could have stayed where they were.
Australia had very low numbers of COVID at the time those decisions were taken. Trying to keep it out of the country honestly made a lot of sense in my view. We have a huge advantage of having no land borders and so it's easier for us to secure our borders than most nations. Border security, in general, is a cornerstone of Australian security in all areas.
What was indefensible, in my view, is that some states closed internal borders as well, and/or imposed quarantine on people arriving from other states. That isn't supposed to be constitutional but the complicating factor there is that Australia's constitution was deliberately written by the state governments to give them power over the Federal government, which was designed to be weak, except in a few areas (defence and foreign relations basically) so when the states did this, they were able to get away with it. Most of what was done there was almost certainly unconstitutional but state Supreme Courts prevented the cases getting past them to the High Court of Australia. Exactly how that was allowed to happen, needs to be fully examined and understood - and that process is happening now.
In simple terms, in a lot of ways, Australia should actually be seen as six separate countries - the six states still have an extremely high level of sovereignty in their own rights. Federation in 1901 was voluntary and they didn't choose to give up much at all. Significantly, during the pandemic, "public health" is almost entirely controlled at state level, not Federal.
And Victoria and Western Australia are pretty much hard left totalitarian states when they want to be - in Victoria, this emerged as an extremely long lockdown. In WA, it emerged as an extremely long near total border closure to the rest of the country. The rest of the country really isn't like those two places - but it's a spectrum. (There are two territories as well as the six states - they have a lot of similarities to the states, but much less actual sovereignty).