There definitely exist "accountable" AI models. Things like decision trees and various types of regressions.
The thing is though... any sufficiently advanced AI is going to be unaccountable pretty much by definition. It's like, calculus is an extremely useful tool for predicting the temperature of a cooling object over time, but good luck explaining to a 3-year-old how to perform the necessary maths. The fact that they can't comprehend it doesn't mean that calculus isn't useful, it just means that it's beyond the 3-year-old's ability to intuitively grasp. In this smilie we're the 3-year-olds. :)