I think you're reading too much into that wording. Do you really expect him to say 'we didn't bribe Dundee but we can't speak for anyone else, like Celtic, doing so'?
I'd expect the SPFL board to actively try to persuade every club to vote in favour of the proposal. It's their baby. They think it's in the best interests of the majority of the clubs or they wouldn't be making it. And they don't want to spending the clubs' time and money voting on a second or third proposal.
It's not even clear to me that the Board of the SPFL needed to put this to the vote. That clause from their Articles suggests it's within their powers to decide on anything not already covered by the rules.
Dave Cormack says, 'Aberdeen were going to vote against the proposition but, when we heard that it would have been a wasted vote since the target had already been met, we changed to 'yes'. Don't want to be seen as not being one of the good guys.'.