Yeah I'd suspect slowly charging up a battery with the bike generator and then quickly discharging the battery to boil the water would be quite a bit more efficient.
If it takes an hour to charge the battery or an hour to boil the water, it still takes an hour. Based on the previous comment of generating 60W, how much battery charging will that do? I'm really asking as I don't have the info at hand to do the maths. I'm assuming choice of battery comes into play.
I think that what they are saying is, if we remove the heat losses from the 1 hour boiling time and instead boil it in a burst of 5 minutes using a battery you would need significantly less energy overall. As a result, using a battery instead of directly utilizing the bicycle's electricity, would take significantly less time.
Internal resistance of the battery would be a significant problem, you'd need a fairly sizeable battery, and most lithium ion cells have a maximum discharge rate of around 1-5C unless they're high-discharge-rate cells which are usually more expensive and lower capacity.
Using a vacuum flask would dramatically lower heat loss.
Some cheap lipo cells can get you a sweet 60-120C discharge rate with a pretty okay capacity. They are also widely available on the used market, usually sourced from EV batteries or energy storage packs. But yes, for the typical 18650/cylindrical li-ion battery, this wouldn't be especially feasible at all