Careful reading indicates the ‘fakes’ simply do not meet the standards for ‘extra virgin,’ not that they aren’t olive oil, although there are mixed oils, some labeled so.
And Italian brands may not be actually Italian olives. Most of the studies crying ‘fake’ are themselves conflating issues.
Extra virgin olive oil goes rancid and doesn’t take heat well, so there is incentive to alter it.
California olive oil seems less likely to be ‘faked’, and Walmart’s Kirkland and Trader Joe’s are known to be reasonably priced good stuff.
“Trader Joe’s”
As a side note - Aldie’s acquired Trader Joe’s in 1979. I can only assume that the Pure virgin olive oil there might pass the test as well.
There is an Aldie’s under construction in my little burg. When it’s completed I’ll have the opportunity to see what the buzz is all about.