You aren't going to see true threadles in AKC agility unless you enter ISC classes...or throw one in there yourself on a FAST course.
I do not believe you will find it in the rules specifically using the term threadle since this would require extensive definition as to what constitutes a threadle. However, it is essentially prohibited by the minimum distance between obstacles, approach angle restrictions and spacing recommendations for what they call 'wrap around jumps' (weird terminology but essentially a component of a threadle). It's not that they strictly prohibit it, but rather that the course design recommendations are such that threadles would never make it through course review for non-ISC courses.
Backside jumps aren't so clearly prohibited though. I think the reason for this is that there are widely varying perceptions as to what constitutes a backside jump. I have seen backside jumps in AKC Masters level courses, but they were placed such that you did not have to handle them as backside jumps. To the judge or other people on course it could simply have been an offset obstacle-jump 180, but I chose to view it as a backside to gain a handling advantage.