This might be possible for a few reasons:

1. Quality index is the ad’s performance relative to competing ads. High CTRs might be considered low quality if competing ads have relatively higher CTRs.
2. CTR can fluctuate on a daily basis. Since the displayed CTR depends on the chosen date range, any “small” date range might show a CTR that seems out of synch with the quality index. Quality index, which does not change with different date ranges, is more of a historical score that will smooth out daily CTR fluctuations. Quality index is also updated daily based on yesterday’s clicks and impressions.
3. Quality index is composed of both expected performance and historical performance. As the ad receives more impressions and clicks, historical performance starts to influence quality index more.