> One of the problems with the process so far is that it was not secret

As far as i can tell, this is a straight up lie. Union organizers might know, but legally they are required to keep who signs a union card secret.

If voluntary recognition happened, as far as i understand, part of the process would be for a neutral third party to verify the signed statements. So if someone was pressured, the verification person would call them up and ask if they really meant to sign, and they could just say no. [Ianal, this is just what the pro union people are saying on wikipedia]