The DoE doesn't pass any laws; it enforces the ones passed by Congress. And as it's a cabinet-level department, Congress approves all cabinet appointees, so blame them on both fronts.
The Department of Education (or ED, not the "DOE") is run by the executive branch. You seem to have skipped that part for some reason. True, the laws and appointment are granted by Congress, however the day-to-day operation and many details of "how" the law is to be implemented do not reside with them.
Speaking with 10 years of experience in public K-12 schools, blame lies with the superintendent. Superintendents are the leaders of a district, and they can and often do set a strong tone of expectations that are carried out by administrators, including principals, which then trickle down to teachers and support staff. There's no doubt in my mind that the superintendent, tacitly if not directly, created this cheating culture in Atlanta. We can blame the law all we want for encouraging the genesis of such an environment, but that's like blaming cheese for mold growth. Yes, an optimal environment was created for this cheating scandal to take root and grow, but it was disgusting school leaders like Dr. Hall that caused it to happen.
I agree with the principle of this (pun intended), but I also think that laws can be implemented in ways that do not encourage cheating on this scale. It's not just the Atlanta school system trying to game the system and get more money and raises (presumably that is the end goal?). Look up Philadelphia, Clarksdale MS, and Louisiana - those were what I found just with a quick google search.