I use the same technique all the time, but I frame it a little differently, especially when I need to convince a client of the merit. Most business people have finally come around to believing in the practice of telling a story as a good way to capture attention while persuading a prospect to purchase a product or service. So, I explain story-telling. Reminding them that there’s no story without a conflict or an obstacle to overcome. The flaw, or to use your term “damaging admission” becomes the obstacle. Of course, the story then goes on to tell how the obstacle was overcome, or how it may seem like a negative, but is in fact a positive.

Sorry to hear about your iPhone.

Bob