Do whites get to decide whether Aboriginals can drink in Australia?

I'd heard before that alcohol was forbidden in Aboriginal lands in the Northern Territory. Until today, I'd always thought it was because the Aboriginals had voted those restrictions on themselves. This would have been similar to the US, in which certain tribal communities have decided amongst themselves to forbid alcohol on Tribal lands (for example, the Navajo in Arizona, Utah, and New Mexico). Then today, I read in the New York Times that it's whites who make those decisions in Australia. Did I understand my reading correctly? 

https://www.nytimes.com/2023/03/12/world/australia/alice-springs-alcohol.html?te=1&nl=the-morning&emc=edit_nn_20230313

...“For 15 years, I couldn’t buy a beer,” said Mr. Shaw, a 77-year-old Aboriginal elder in Alice Springs, the territory’s third-largest town. “I’m a Vietnam veteran, and I couldn’t even buy a beer.” Mr. Shaw lives in what the government has deemed a “prescribed area,” an Aboriginal town camp where from 2007 until last year it was illegal to possess alcohol, part of a set of extraordinary race-based interventions into the lives of Indigenous Australians.

Last July, the Northern Territory let the alcohol ban expire for hundreds of Aboriginal communities, calling it racist. But little had been done in the intervening years to address the communities’ severe underlying disadvantage. Once alcohol flowed again, there was an explosion of crime in Alice Springs widely attributed to Aboriginal people. Local and federal politicians reinstated the ban late last month. And Mr. Shaw’s taste of freedom ended...For those who believe that the country’s largely white leadership should not dictate the decisions of Aboriginal people, the alcohol ban’s return replicates the effects of colonialism and disempowers communities. Others argue that the benefits, like reducing domestic violence and other harms to the most vulnerable, can outweigh the discriminatory effects."