The problem is, laying in the road, injured after being knocked down by a car, or (random other example) after you have had a driver bullying you off the road, is not the best time to construct a calm explanation.
In fact, that kind of proves Arch's point. Just like the Driver of the car having a go at the injured cyclist, we may not react at the best of our abilities after an unfavorable altercation.
Yep, agreed. However, if someone was lying in the road injured, hurt then I as the officer on scene wouldn't really be looking to get much more than a basic 'What happened' - and I'd be asking paramedics if it was ok to ask this first. Primary issue would be the casualty. No decisions would be getting made at the side of the road in the case of an injury that could be serious or require hospital treatment, so the full (and calm!) explanation could wait until later when the casualty is recovered and comfortable.
This would, and should, be the same whether you are a cyclist, a pedestrian or a motorist.
If you are unlucky enough to get a copper who is willing to start arguing and blaming a casualty while they are still lying on the road, I'd suggest that's a problem regardless.
To sum up, I'm not suggesting you have to explain the basics of cycling straight away at the scene, but be aware it may be useful to do so later, when you've recovered and are giving your full account/statement.