I had an opposite experience in Texas (semi-rural Texas no less). The gifted and talented programs (i.e. things sometimes referred to in other districts as "Quest", "Omega", etc...not AP as occurs in later grades) did the exact opposite of focusing on standardized testing. The vast majority of time was spent on "above and beyond" and critical thinking. Granted you tested into it and all of your time was not spent there, but even times in standard classes were not heavily focused on standardized testing.

This goes to show that the problem is more localized than state level, it is a municipal and district-level choice so long as you meet minimum testing requirements. Now when students don't meet minimum testing requirements, most districts unfortunately fall into the trap of teaching to test as opposed to teach.