Stamped 350w, it isn't; however, the 350w and 250w are identical apart from the marking, so you might be able to argue that it is legal as long as you set the current to 15 amps and the speed to 15.5 mph. The other way round, if you took the 15amp 250w BBS01 and set the current to 18 amps, it would be the same as the 350w one but legal.
One guy took a 500w BBS02 and swapped the motor and it's housing from one main drive and casing to the other along with the controllers, so he had the 250w markings on the motor. The casing with the markings on is the same part on all versions of the BBS01 and 02. Basically there are mainly 4 versions with two different controllers, each with two different settings, and two different motors. One motor is wider than the other and has thicker wire.