It's not a good Idea to leave lithium batteries on a charger unless you are there if something goes wrong. More that couple of burning batteries have been reported on this forum. Especially a battery in questionable condition. That will dramatically increase you risk of fire.
In theory yes, in practice no.
You lap top, cell phone and other devices all have lithium ion batteries, they are all are just as likely to have the same slim chance, to catch fire. So unless you attend your cell phone and lap top when they are on the charger the PV battery is no worse.
Your best solution if this does concern you is to charge them on a hard non flammable surface. The plug on the top of your stove is a good choice. Or if you want to be very very protective, in the oven (of course not turned on)
Reports of blowing up batteries can often be attributed to mis-charging with a device not made for the battery (a 510 battery on an eGo charger) a non-protected mod battery being charged on a charger with no protection or at a higher voltage than recommended. There are also reports of lap tops exploding, with video that can be view on YouTube.
Commercial batteries on the market such as Joye eGO's offer protection circuits to prevent the battery from reaching conditions where it can explode. Nothing is fool proof, but charging batteries in an empty ammo box in the fireplace only when you are watching isn't necessary.
100% by the book, Lithium Ion batteries should be discharged fully in a brine mixture before disposing of, because a low voltage condition can cause the batteries to catch fire. This is not put into practice very often, and we do not have garbage cans exploding across the country.
