Read the fine print on the link:
Identifying an affected battery
Affected batteries will have one or more of the following symptoms:
* Battery is not recognized causing an X to appear in the battery icon in the Finder menu bar.
* Battery will not charge when computer is plugged into AC power.
* Battery exhibits low charge capacity/runtime when using a fully charged battery with a battery cycle count (as shown in System Profiler) of less than 300.
* Battery pack is visibly deformed.
Even though they were correct in telling you that your battery is not covered by your extended applecare, call them back and explain politely that you have 199 cycles and 20% health, or take it to your apple store. They will provide you with a replacement battery.