If he falls, an injury is more likely because the greater weight puts more stress on the same bones.
However I don't think "plus" always = "out of shape". I also have seen "plus" riders to be very good riders with the great seat and hands with happy horse carrying them around. And those who take riding seriously (whether "plus" or not) will ALWAYS care for the horse well-being. So personally I'd say yes, the big chunk of that article sounds quite insulting.