Have you tried unchecking "autostart"?
I believe the free running option tells the video to continually play...which allows multiple scenes to access the material and they will always be in sync, which sounds like the behavior you are looking for.
If you have auto start checked on as well, it may be competing, as it will try to start your clip again from the beginning if the scene goes online, which will make it out of sync. Likewise, if you have the clip on the scene director it may be competing, as you are telling the clip to play there as well...
Not sure if this will work for you, but it's worth a try!!
#XPression