well, the long and short of this, is;
Yes, if it is saying bad battery, the unit is played out... i.e., no it ain't registering "---" on the dash, but it' hot, power wise...
NOW, comes the dealership, and their participation... we have seen many just turn customers away... basically flipping the bird to them... unacceptable.... and even "lying" to the covered customer, without ever lifting the phone to make a call... I hope ALL those dealerships disolve into dust.
you have an extended KPP plan, you ARE covered... however, you will likely get a new style enor... no big deal, the new ones have a larger ampacity batt already installed, and should lat better than 5 years. (even tho they are not replaceable like the gen 1 version, if you decide to do it on your own)
I had mine replaced, on my '08, which was purchased 7-7-07, in late 2012 (10-2012), under my extended GTPP/ KPP... with no issues, in a different state from my original purchase... I made a call, explained my need, and they called me back after ordering the parts without even seeing/leaving the bike, to have me come in and have them done when the parts showed up 4 days after I called. Dealers can hose you down, or they can be good people... lets hope your dealer is the latter of the 2.
But, a far a "Kaw" is concerned, with a KPP, it IS covered... replacement due to age of some "projected 5 year value" that was originally noted, as normal battery life on pre '13 models, does not come into the equation with KPP.
call, schedule, have them replaced, cost free.. if you need tires... well, add those in, you get free mount and balance but you pay
their tire price if you buy their tire... and they can jack you again, if they are determined. (so buy tires online, and carry them in also... be prepared to take your old ones home with you tho, they charge for "old tire disposal"