There is no consensus that implied multiplication has a higher precedence than ordinary mult/div. Very few people defending the answer 1 even mention that they're viewing a(b) as a higher priority operation than a(b). They just mumble something about the P in PEMDAS meaning you evaluate parentheses first, but they don't understand that means *inside the parentheses, not stuff "attached" to the parenthesis by an implicit * operator.
The question is whether a(b) is the same as a*(b), or whether it's a magical new operator like * but with higher precedence? If it's a new operator, we have to rewrite PEMDAS because it doesn't include any "special implicit multiplication" in the ordering rule. Does it go before or after exponents? Without knowing that, we can't evaluate:
ab(c)
Nobody reputable I can find believes in this magical new operator theory. At best they're just saying it's ambiguous to avoid getting flamed. Ambiguous how? Either a(b) is a new different kind of mult operator or it's not. From wolfram alpha to google to HP and TI calculators, everyone who implemented those agrees that it's a*(b) so the answer is 16. So far the only implementation I've seen that gives 1 is (some?) casio calculators. Not a surprise that Casio doesn't have the most rigorous order of operations evaluation.
I believe the reason it's so confusing to so many people is that a situation with "a <operator> b(c)" usually only happens when <operator> is addition or subtraction. Therefore people get in the habit of evaluating the implied multiplication in "b(c)" before they evaluate <operator>. But it's not correct to extend that to the case where operator is division.