Although they can't require that you go to the dealer for maintenance, the burden is still on you to prove maintenance was done.
I am not sure that is true. The burden is first on them to prove that lack of a particular maintenance could [reasonably] be the cause of the particular problem (at least, that is my understanding). If it could be, then you do have to somehow show some type of proof.
Not having proper valve clearances, for example, causes very particular issues.
This doesn't mean the dealer couldn't just reject you outright, or even mama Kawasaki reject your claim. It is more of a "if it ends up in court" situation. One hopes it never would need to get that far.
As far as the valve deal.... the odds are extremely low on a C14 that not having it done at 15K or 25K or even 50K would cause any damage because them getting out of whack enough to cause damage appears to be very, very rare. This is a testament to the good design they used, and there are tons of posts here over the years showing the valves typically still being in the tolerance zone for way more than double or triple the recommend USA check/adjust interval.
[...]Having that information will look a lot better than saying "well, I did it myself, and no I don't have any proof, but I swear I did it properly".
Very true... good record keeping is good.