Actually, when bitcoin goes down people are in fear and they also attempt to sell other altcoin too, cause they believe in bitcoin most but don't believe enough altcoin. people do panic selling that's why all crypto market goes down in a sudden after btc dump. that's why you will see when bitcoin goes down 1x, another alts are goes down 10x fold, all of this are happened for panic selling.
One reason might be that whenever the market goes down, Bitcoin also represents the exit currency when they want to sell, thereby also putting pressure on the price. Bitcoin is also the best indicator we have when the whole market gets into trouble. It would usually hit Bitcoin first. By now there are USDT pairs but who knows what is going to happen when one day there is some kind of bank run on USDT because Bitcoin dumps hard. Nobody knows what the reserves look like for USDT and whether they could serve all customers in a quick fashion.
So generally I would say that yes most of the coins are dependent on Bitcoin, maybe not entirely but to a significant degree.