When I went to Cozumel, I was a pretty new diver with very little experience in currents. I had no trouble at all with the down currents that we experienced.
Since then, I've experienced some real,strong down currents and washing machine currents. Pay attention to the instructions of your dive guide. There is usually a trick to diving the spot which will make it fun rather than frightening. We really enjoyed the washing machine in Galapegos, it was like an amusement park ride. And, in Africa, we got into some crazy currents going every which way. We paid attention to our depth and had a fun ride. At the end, we were all scattered across the bay like balls on a pool table and just sat back, relaxed, while our DMs picked us up on the pangas. Thank goodness for SMBs! Took 90 minutes to pick us all up.
Down currents are all about the method. Don't try to fight them. Get away from the wall, or if you really can't, than get closer to the wall. Usually, that's all you need. You may need to use your BC for lift but be careful that you don't fly to the surface. Same with dropping weights, I wouldn't, unless its a last ditch effort.
Finally, keep an eye on your gauges. I think what really got the boy in the video is narcosis. He didn't know he was deep until he was too deep and than the effects of narcosis probably contributed to his panic.make sure you stay above 100 feet if you have a chance of down currents because 130-150 can sneak up in a hurry. Narcosis can have strange effects. If you've never experienced it, the middle of a down current isn't the best place to try it. Better to stay out of narcosis range so that you have your brains about you to problem solve when needed.