I've always carried them on the table but you're right, those security measures that can prevent you from burning your house are never too much. The important thing is to have a CO2 extinguisher, remember that it is a chemical fire. A multipurpose fire extinguisher ABC the only thing you can get, apart from putting everything full of ****, is to spoil the electronics that you may have nearby.
Always try to be close when loading, never leave them unattended. Never leave them fully charged for more than 3 days. That's what the storage function is for. Store them in a dry and cool place. Complying with these simple rules of use, you extend the life of the batteries a lot.
I've got today some accessories and one of those was an extra battery (an original one). The first thing i did was to check if it was in store mode ,and it was ( 3.83/3.84 V in each cell) then i've looked at the IR ( 6,8,7,9 +- 2 mohm ). last i've had a look at the small paper inside the bag and it said " in the event of a fire , a Class D, dry chemical fire extinguisher must be used " . The class D is for combustible metal right ?
So probably is good to have one D class and 1 ABC class for everything else can catch on fire .