Just because the tire is rated for 112MPH doesn't mean it's going to immediately explode at 113. I got a reckless driving in my Charger way back when I was still young and immortal. In the comments box of the ticket was written "radar indicated 146MPH". That's 34MPH higher than the speed rating of my tires, and I'd been going that fast for a minute or two. Nothing happened. I'm still here.
Do I recommend such behavior? Absolutely not. Have I been that silly on more than occasion? Years ago, yes. I've never suffered a speed-related tire failure but I'm sure others have.
I believe the speed rating is based on a sustained speed, i.e. "travelling at a constant 112MPH" rather than "Never exceed this rating ever or you will die." I could be 100% wrong about that. I do know that it's mostly a CYA measure for the tire companies to limit their liability. Regardless, those F.A.S.T. competitors are above the speed rating for only a few seconds.