Battery still drawing tiny current when fully charged
Addressing your concerns in turn:


Battery damage.


All depends on how good the battery charger is. The best treatment for a lead acid battery is to maintain a trickle charge after recharge. The best treatment for a lithium ion battery is to cut the charge to zero. The charger could be doing either and still be drawing 20mA for its own purposes.

The manufacturer could care about battery life or they could not. Whether its causing damage is probably up to how much you trust the manufacturer!


Fire risk. 


Certainly not while operating correctly and only drawing 20mA, but anything left on is more risky than being physically switched off.

In general, I sympathise with the concern but think it's not worth worrying about:


20mA @ 5V is 100mW and wont make a dent in the grand scheme of things. Charging from another battery is its own issue.
Whether the battery is being treated well or not is really a product quality consideration - is the product well made and likely to last a couple of years? Then the battery charger is probably well made too and nothing to worry about. Is the product crappy and likely to be chucked out in a year? Then who cares if the battery only lasts 2 years?
Of all the things that could catch fire, is this one likely? Probably not. Consumer products have safety requirements to meet, and there's bound to be someone that treats the product worse than you that will be the first to prompt a product safety recall.


If you're not satisfied, then join the campaign against Phantom Power - there are plenty of guides, tips, products and advice associated with reducing phantom power. You can use automatic detection, timers, rules and triggers to turn off devices, but it's a rabbit warren to navigate. The Lawrence Berkeley Laboratory's Standby Power site is a good place to start - there's even a chart with battery chargers on it.