That was just a guess based on how long other roughly human shaped robots (like from Boston Dynamics) last untethered. Unless Elon has invented a new type of battery or more efficient servos specifically for this robot.
So, the BD humanoid weighs around 190lbs. The first gen Optimus weighed about 160lbs. That was all COTS machinery. The Gen 2 weighs about 20bls less. As for batteries, I would expect they chose one specifically for performance and weight over robustness, since what a bot encounters would be far less dynamic than an automotive environment.
As for servos, why yes, they did. Part of designing for manufacturing is bringing things in house where your design teams can work together to optimize performance and ease/cost of manufacturing.
So, for assembly line type work, where it only has to walk around once in a while, it could stand on a charge point. At home, if it gets a an hour or two, and can top off from outlets where stationary tasks are commonly performed like the sink or bathroom, I think that's workable.