Can't speak for Acura but that statement is incorrect for lexus and infiniti.
I am by no means a car guy, and their engines may be the same but the luxury isn't even close when u compare a fully loaded TOYOTA or Nissan to a inf or lex...
It's all a facade. In Japan, there is no Lexus brand name, until two years ago. They were selling "Lexus" models under the Toyota badge in Japan.
Back when the NSX was exported, it was sold under the Honda badge in Europe and Asia, and only in North America, it was rebadged with the Acura name. The same exact car. The American Acura TSX was the European Honda Accord.
Now, most of these brands try to not sell the same body style under their regular and luxury brand names in the US so they aren't internally competing against each other, i.e. cannibalizing sales.
As for Lexus, the ES has been a rebadged Toyota Camry for the longest time. Not until 2013 did they start sharing less parts. The US Lexus IS models are known as the Japanese Toyota Altezza models. So there is no comparable Toyota model to the Lexus IS because they don't want to have internal sales problems. Also, the Scion brand name is basically a rebadged Toyota. The Scion xB doesn't exist in Japan, but it is a Toyota bB.
The Lexus name brand didn't exist in Japan unitl 2005.
The Infiniti name brand didn't exist in Japan until 2013.