I also dislike their implied claim that it's all experts in planets:
We, as planetary scientists and astronomers, do not agree with the IAU's definition of a planet, nor will we use it. ...The list of signatories have studied every planet in the solar system, asteroids, comets, the Kuiper Belt, and planet interactions with space environment.
The first sentence reads that everyone on the list is a planetary scientist AND astronomer, and the second listed reads that EACH signatory studied every planet. No, simply not true.
As for 300 names, keep in mind that put a piece of paper in front of enough people and you're bound to get people to sign it.