I think everybody is overreacting.
First of all, lithium batteries do catch fire, although usually the battery has to be damaged or defective in some way for this to happen. Lithium itself is extremely flamable. It's rare, but it does happen. There are numerous documented cases. This isn't some urban legend. Remember the huge Dell and Sony battery recalls?
Second, you can check any number of batteries, as long as they are within the unit they power, i.e. you can check a camera with an installed battery.
Third, there is no limit to the number of carry-on spare batteries as long as they are each under 100 watt-hours in capacity. For comparison, a P45 or 1DsIII or D3 2500mA/H battery is roughly 20 watt-hours. Even most laptop batteries also fall under this limit. For example, my laptop batteries are 40 watt-hour - well under the limit.
Fourth, you can carry on up to two very large batteries that total 300 watt-hours of capacity. These would be some pretty massive batteries.