There is a known situation with some video editing software exported videos having sync issues. This happens due to a live broadcast dropping frames during internet fluctuations and some exported videos not being capable of handling variable frame rates.
To fix this issue you'll need to convert the file using a program called HandBrake. It can be downloaded HERE for free.
When you open the software you'll be prompted to choose/open the video file.
Next choose the destination to save the file to. By default it'll save to your Movies folder.
You will now go to the Video tab in the center of the application and choose Constant Framerate. (See Image Below)
Handbrake will begin to convert the video into a new file. Depending on the length of the clip conversion can take a long time. Expect the conversion to last up to the duration of the clip.