You are right. The answer is one. The way we were taught is that 8 is divided by a number. But what is that number? It is 2(2+2). Before you can divide 8 by the second number you have to determine its value, which is 8. If you separate the first 2 from the equation, it becomes a different equation with a different answer. For them to come up with 16 the question would have to read what is 8/2 X (2+2).
Ah, but that is what the problem DOES read. The implied multiplication operation between the first '2' and the parenthesized (2+2) is not somehow granted higher priority than the division that precedes it. It's just a multiplication. It does not bind the '2' any tighter for the fact that it's implied.
The simple fact is that the problem is intentionally stated poorly, in order to encourage ambiguity and multiple interpretations.
The other simple fact is that the rules of order of operation are by agreement for the sake of notational clarity. One could construct a different set of rules, and as long as it was consistent, it would be valid.
But mathematicians have agreed upon one set of rules, and it's best to abide by them if you want to be understood accurately.