There is no law that says you can't stop your vehicle in the middle of a road (given, as TD says above, you weren't intentionally trying to cause a crash). This may be for entirely spurious reasons - like "i saw a cat crossing the road and didn't want to hit it". And, given that you *did* hit them, you were (at a minimum) following too close, or operating without due care (which is careless).
As for insurance covering - of course they will cover. You'll just be 100% at fault, and have to pay 100% of your deductible. But it sounds like you didn't have "all perils" coverage, ie: minimum. So yeah - you're out 4k. I'd just report it to a collision reporting center, then take your bike to a shop and see what they can do. Might be less than 4k to repair. Since you're not reporting it to your ins company (you don't have to, since you've reported to collision) and not made a claim, your rates should not go up.
I'm actually kinda fuzzy on this. I had almost the same thing happen (except i was stopped for a good 10 seconds in the car when someone ran into the back of me) and was judged 0% at fault. Car was a write-off, but ins gave me money for it, even though i had minimum coverage, because it was my primary vehicle.
What i'm fuzzy on is - if you're 0% at fault, and an insurance company asks you "had any claims", what do you say? I usually respond with "1 0% at fault accident" and let them sort it out. But it bugs me that i don't know the proper answer to this.