In my experience, barring truly mentally challenged children, most children classified as 'dullards' by the education system just don't understand how to cope with the traditional model of teaching. Once someone takes the time to understand them and teaches them how to 'work the system' while still learning, or once they themselves realize that they can take things in their own hands, they shine. I have seen this time and again with cousins, friends and a bunch of kids my mom taught when I was growing up (She is a teacher).
So, if the public school teacher thinks your child is a dullard, it may be a much wiser investment in my opinion to consider educational institutes that will pay a bit more attention to the child's needs. In fact, it may not even take that, it may just take one good, concerned teacher to understand why the kid can't cope, gain their trust, and then teach them how to get the most out of the existing system.
All of this is IMHO, and I am not a teacher, just someone who has seen a lot of kids suffering because of how they were labelled as dullards and subsequently ignored for years by teachers AND given up on by parents. I have also seen 'dullards' change course and shine, once they had the right help.