Bless 'em, the BBC are not the place to look for stats. They don't even compare it to anything. Is 18.5% good or bad? And they go back to '92 when the gap between the leagues was far lower than it is now. Not to mention they don't standardise for fixture difficulty, or separate home from away games, or weight for final league position, and so on.
Put it this way, over the last 5 years the win rate for promoted teams general is 20% over the season, but on the opening day it was 33%. And if we just look at home games, the win rate was 45% on the opening day for promoted teams. So at the very least, there's a bit more to say than that Beeb article would suggest.