Division is usually written in fractions

Division and fractions aren't the same thing.

fractions which has an implied set of parenthesis

Fractions are explicitly Terms. Terms are separated by operators (such as division) and joined by grouping symbols (such as a fraction bar), so 1÷2 is 2 terms, but ½ is 1 term.

8/2(2+2) could be rewritten as 8×1/2×(2+2)

No, it can't. 2(2+2) is 1 term, in the denominator. When you added the multiply you broke it into 2 terms, and sent the (2+2) into the numerator, thus leading to a different answer. 8/2(2+2)=1.