I've sprained my ankles so many times I've lost count. I had bad ankles to begin with and they haven't improved with time. I can't say my sprains have ever been caused by blood in the wrong place.
Also, I have to question what is really a sprain in the classic sense and is everyone using the same definition. I don't mean you step in the wrong spot and your ankle is sore for a day. As Cat, said, sprains are torn legiments and they simply don't heal by the next day. Having said that, sprains do vary in seriousness so it's hard to compare, especially if you don't go to the doctor. Personally, I've had so many, I don't usually either unless it's been more than a month.
My foot and ankle and leg above usually turn dark purple or black by the next day and stay quite colorful for weeks. My ankle swells to at least twice the normal size. If you're going to use heat, you better use ice as well, which is much more effective. If your skin really does develop a deep bruise, we are all entitled to our opinion, but it won't be gone the next day, no matter what you do. If it is, it truly is a miracle.