Hi,
I've been outright refusing to use batteries with lithium chemistry, [...]
I take it that you have no cellular phone, no PDA, no new powertools etc. then?

A car can be extremely dangerous... If there's an idiot behind the wheel.
A bread knife can be extremely dangerous... If the one holding it is a psychopat.
A lithium battery can be a bit dangerous... If you are careless and give a damn about proper charge/discharge techniques.
I have used lithium batteries for a vast range of apps during a decade+ and so has my friends and coworkers and neither them nor I have experienced even a single cell catching fire (yet, at least).
Staying within the manufacturers nominal parameters is the key - don't let horror stories scare you off of the benefits lithium technology brings. With millions of Lithiums in use every day and only a few verified stories about lithium "explosions", I'd say it's much more dangerous to drive a car (even if you leave the idiot out of the equation).
The important things to keep in mind with lithiums are... Charge current, end-of-charge voltage, discharge current, end-of-discharge voltage and cell temperature. Keep within manufacturers specs and you have a lightweight power source.
And don't open them of course!!
The Iron Lithiums are considered the safest (although some will surely translate this to "can be treated worse"), but are a bit heavier per capacity (nothing like Nickel based cells though).