The OEM e-bike charger and battery, unless damaged, are practically risk-free if used in specified ambient conditions (i.e. not extremely hot or cold or wet) and disconnected when charge is completed for extra margin of safety. The danger is certainly lower than other common situations (e.g. 5 gallons of gas in container in garage).
However, some Chinese suppliers cheat and skimp on the electrical safety components that monitor charging conditions on the battery. So if sensors that detect battery cell temperature are inferior or missing, it won't shut off the electricity causing the cells to overheat and rupture. Some e-bike batteries are completely missing the safety components. Buy from a reputable e-bike manufacturer, and don't buy cheap replacement battery packs (there is a reason why cheap clones cost a quarter of the oem pack).
“...practically risk-free” still worries me, as does getting fried in a house fire.
BMW & Audi are having their EV problems, too:
https://www.autoblog.com/2023/12/26/porsche-audi-recall-plug-in-ev-chargers-over-outlet-fire-risk/
“The OEM e-bike charger and battery, unless damaged, are practically risk-free if used in specified ambient conditions”
Sounds as though NREL doesn’t agree, or they would have allowed charging with the above constraints.