Jumping from a Car Battery with engine off is not an issue the Bike will only draw what it draws but if the Car Engine is running you risk it's charging system over whelming the Bikes Electrics.
This is not a 100% outcome but the risk out weighs the gains.
It did blow the fuse after trying to cook the Battery, I suspect it went up in flames for an unrelated issue but we will likely never know, Maybe if it hadn't been jumped from a running car he would be flying down the road without a care n the world, Maybe
I know a bike doesn't need much amperage compared to a car, so even a fair car battery should be much more than a bike needs, but a properly running car should be somewhere near 12.8~13.X or somewhere around there, maybe 14. That shouldn't be a problem at all for a bike.
In addition, it shouldn't draw any more that the device calls for. If I understand it correctly, a starter motor, in proper condition, can't draw more power than it actually uses. If the small bike starter is 1/3 that of a car (wild guess) that doesn't mean that it will all the sudden be able to draw all the amps from a car battery or as much as a car starter would.
It's like a turn signal bulb, if it draws 1 amp, that's all it can draw, unless it's shorted or somehow defective. And if it does draw more than it's rated for, it should pop a fuse instantly as the fuse is designed to be the weak link in the chain.
The safer setup is to actually let the bike's battery take a charge from the other source for a while, charge itself up and then start the engine, maybe by itself, if it can. I think that's how some of those tiny jump-boxes are supposed to work, the charge up, very quickly, the low battery. That way the don't need the high discharge batteries which are much more expensive.
BTW, any idea on where I can get a pic of the wiring diagram on an 05 ZX6R? I need to fix someone's bike.