Interesting.
I’m not going to gainsay the mathematician, but I was never taught either acronym, or the left to right convention.
What I was taught was that, the number in front of the parenthetical always applies to the parenthetical. Ditto an exponent, FWIW.) IOW, X(N) is always calculated as a single number first, X times N. Then, if you see something like the problem posited, you read it like a fraction: 8/2(2+2). That can’t be solved as 16, just as 1.
To get 16 out of the 8÷2(2+2) equation, you’d have to read it as (8÷2)(2+2), but that would violate the rule of grouping the parenthetical with its multiplier.