A bad slide that works because the SS drops the ball is still a double. A double is not contingent on the quality of the slide or how well you hit the ball - it is defined by making it safely into 2B. That happened. Whatever happens after that should be immaterial, no matter if it happens two tenths of a seconds, two seconds or two minutes later.
Here's how I see it:
In both cases it isn't egregious enough to be an error but the player still failed to complete a close play because of pressure from the opponent, thus the credit goes to the opponent. In one case, the fielders couldn't complete the catch & tag because they rushed knowing the runner was closing in fast, thus the runner gets credit for the double. In the other case, the runner makes a mistake sliding in too aggressively/wildly to beat the tag but he likely only beat the tag because he made a slide that he couldn't complete, thus he doesn't get credit. He was never truly safe because he was never in control. The situation where a guy rounds a bag is different because he passed the bag under control and uncontested.