No claims discounts are (kind of) a swizz, because they don't affect the actual premium, they are a % discount on the premium cost. So if the premium goes up, even if you have protected the discount, the price you pay will still rise. Here's an example.
Year one - premium = £100, no claims discount (protected) = 60%, price paid = £40
Year two - premium = £200, no claims discount (still protected = 60%, price paid = £80.
Your NCD stayed the same, but the price you paid still doubled. This is why it is a swizz, because it doesn't stop your premium rising, but only kind of a swizz, because it does still save you a wodge of money.
Your premium is based on the level of risk you pose - specifically the risk you pose to the insurer that they will have to pay out. One of the key factors they use to determine this is whether you have caused them, or any other insurer, to pay out in recent times. If you have, then your premium will go up.
If your insurer has to pay, then regardless of who actually caused the accident, it will be classed as a fault claim. Having the fault claim makes you higher risk, so your premium will rise (offset by whatever NCD you have).
The only way this would be treated as a no-fault claim would be if your insurers were able to reclaim the cost paid to you from either the bike's insurer (unlikely - if it was reported stolen, they would have no liability) or ride (unlikely - 15 year old joyriders are unlikely to either their own valid insurance or have the funds available).
So yes - if no one can refund your insurer what they pay to you, your premium will rise*, because the claim will be against you as a fault claim and you will be regarded as higher risk.
*unless, as a pp noted, something else has changed in your circumstances or the way that your insurer calculates risk that offsets this. Unlikely but possible.
I really, really hate insurers.