"I saw the brake lights of the car in front come on so, having left enough of a gap that I, myself, could react in good time, I gently applied mine to maintain the gap. Unfortunately, I noticed in my mirror that the car behind was gaining..fast. My brain just had time to register that the front of the car was dipped, like it might do under heavy braking, but the car was not stopping. I was sure he was about to hit me so I released my brakes to increase the gap between myself and it. Unfortunately, this meant that I was a lot closer to the car in front, who had continued to brake. Fearing either a rear end collision from the car behind, or going into the rear of the car in front, I made a decision to lie my bike down...blah, blah, blah...all under control" Or words to that effect.
What we don't know is whether the cop saw what happened, which I think is the issue. If he did, then, possibly, he can use the 'careless' thing. If he didn't, he's just guessing. If he did see it, find out if he rides. If not, and you're feeling up to it, you could dispute his credibility; the physics of a bike and a car are completely different. If you're going to crash, it's far better to slide into something than hit it head on: your slide, therefore, was intentional and under control; you had the presence of mind to make the decision. You could also try to find out if he's ever had an accident which would further undermine his 'expert assessment'.
I'd use this as a last resort, tho, and take Wannabe's advice first.
Glad your well enough to recount your tale, no matter how crappy it is.
Heal quick and well.