Considering the expense of the steps they plan to take, they know this to be a blatant lie! They are clearly worried of losing far more than a few hundred people paying dues.
Even though 40% of members may have preferred RTW, the unions will still be able to get it on the ballot. Signing petitions is like "card check". You'll get two union thugs at your elbow with the petition shoved in your face. A lot of folks will fold and sign.