I think there's more to it than that. To label an opinion heresy is to claim that it deviates from the majority opinion, whether or not that is actually the case.
Sort of related: The Bolsheviks were clever to call themselves Bolsheviks; the Mensheviks probably outnumbered them at the time of the split, but failed to contest the nomenclature.
To label an opinion heresy is to claim that it deviates from the majority opinion, whether or not that is actually the case.
I think that's part of the meaning of "private opinion" in the quote. If someone agrees with the majority, they don't have their own private opinion.
Here's the new thread for posting quotes, with the usual rules: