The requirement is only for live streams, that is, streams that do not include the endlist tag. The example in 8.2 is a non-live (vod) stream. Are your streams live or vod? Also, I see that they changed the requirement slightly in the latest spec. The requirement is the last sentence in 6.2.2. Earlier versions of the spec said the playlist must include at least three segments; the latest spec just says that the duration of the playlist must be at least three times the target duration. Nevertheless, I'd recommend that you always keep at least three (preferably more) segments in a live stream.
I don't know what is causing your a/v sync issue. The first thing to check is you should make sure that the PTS values in both the audio and video streams increment seamlessly across the segment boundaries.
--Mark