Rules-of-thumb for noticeable and detrimental asynchrony between audio and video streams have long since been established from the contributions of several studies. Although these studies share similar findings, none have made any discernible assumptions regarding audio and video quality. Considering the use of active adaptation in present and upcoming streaming systems, audio and video will continue to be delivered in separate streams; consequently, the assumption that the rules-of-thumb hold independent of quality needs to be challenged. To put this assumption to the test, we focus on the detection, not the appraisal, of asynchrony at different levels of distortion. Cognitive psychologists use the term temporal integration to describe the failure to detect asynchrony. The term refers to a perceptual process with an inherent buffer for short asynchronies, where corresponding auditory and visual signals are merged into one experience. Accordingly, this paper discusses relevant causes and concerns with regards to asynchrony, it introduces research on audiovisual perception, and it moves on to explore the impact of audio and video quality on the temporal integration of different audiovisual events. Three content types are explored, speech from a news broadcast, music presented by a drummer, and physical action in the form of a chess game. Within these contexts, we found temporal integration to be very robust to quality discrepancies between the two modalities. In fact, asynchrony detection thresholds varied considerably more between the different content than they did between distortion levels. Nevertheless, our findings indicate that the assumption concerning the independence of asynchrony and audiovisual quality may have to be reconsidered.