"On the dock it says 'Use the charger only with the AC adapter provided'."--- Which is a good idea.
The voltage and current is the maximum level the adapter can handle. The need for the correct adapter
is due the "current flow rate", typically in mA/hr. And with Lithium-Ion batteries, that is even more crucial.
Most of the incidents in the news the last couple of years, relating to fires involving Lithium-Ion, were a result
of problems with controlling current flow rate. And many of those occurred during battery charging. It's been
an issue on-and-off with rechargeable batteries for computers, mobiles and portable audio gear since the 1990's.
Kind of occurs in clumps. You can have periods where you won't see a single incident, then a swarm of incidents.
Depends on the product, the battery, the charger and a host of other factors.
So it's best to heed the warnings and leave nothing to chance.