I've conducted several air tests on 300s where asymmetric engine acceleration on the ground was apparent but both engines performed as they should during the airborne slam accelerations which was a bit odd. Also vice versa which was a bit odder.
The solution is a bit engineery and initially required fettling of the MEC and various other adjustments which I can't remember. Ultimately, if that didn't work, changing several of the engine sensors (P6 rings a bell) was the next step. In one case, after about 5 days of engine runs, a complete engine change was required (which is actually quicker and easier than a MEC change). In most, if not all, cases the AT wasn't the issue.
Also it transpires that fitting a new or reconditioned MEC to an older engine can produce similar symptoms.
On the point of not 'helping' the AT achieve the required N1 - no, it shouldn't be necessary but quite often is required to ensure that thrust is set prior to 60kts. If it isn't then your perf. is invalid and you should reject.