Precisely. She had to beg him to heal her despite her inferior status as a non-Jew, ie- a dog who eats of the crumbs which fall from the master race's table.
Mike, the verse is refering to the fact that the food is from God's table, not the master race's table. The point of those verses was to show that Jesus tested her faith, and because of the great faith that she had, he healed her daughter. It was also to show Jesus's disciples that those he was sent to save were not just Jews. Jesus never said that the Jews were the children, and all others were the dogs, only that the food was for the children, and in this case, she was one of them.