I don't see the logic in the claimed reason. First of all, it's not advisable for traffic (either cyclist or motorist) to be in the door zone. Secondly, if the person in the car looks back before opening his door the cyclist who ends up next to the door when it actually opens would be quite a few feet back when the motorist first looks. So he should have a clear view of the front light shining forward with his initial glance. OTOH, if he just opens the door without looking then any light shining sideways from the cyclist won't be seen anyway. The cases I've seen of doorings have happened because the driver was looking forward when he opened his car door - not at all in the direction of the cyclist. By far the most effective light to avoid these would be a bright light shining forward so that portions of the car on the left side and in front of the driver (mirror, left edge of dash, etc.) are illuminated by the beam.
Is there any other definition given for the side lighting beyond the 'visible from 300ft.'? Note that the effectiveness varies widely depending on other ambient lighting or distracting lights in the same general direction. If the light is isolated and on a dark night, human vision can see a single candle at a distance of up to 30 miles (
How Far Can the Human Eye See? | Human Visual Acuity | LiveScience). So very little light would really be needed to see something 300' away under optimum conditions. If the edge of a cyclist's flashlight beam hits any part of his cables, brake levers, front tire, etc. then it would probably be visible from that distance as seen from the side - again, under optimum conditions.
California has had a similar provision for some time (I don't remember any changes in the last 20 years) that requires:
"A lamp emitting a white light that, while the bicycle is in motion, illuminates the highway, sidewalk, or bikeway in front of the bicyclist and is visible from a distance of 300 feet in front and from the sides of the bicycle." Most bicycle-specific lights I've seen do emit a tiny bit of light to the sides (enough to say they comply under good conditions, but probably not very useful in practice). And any decently bright flashlight should be casting enough light on the road and other objects ahead of the cyclist so as to be seen by someone observing the cyclist from the side.