A Maltese (and similar rat breeds) might be small, but their bite can surely make a lot of damage. Strong jaws, the carnivores, y'know. My cat is nearly twice the size of the average Maltese. With canine teeth about 1 cm long. Same for claws. He won't be able to immediately kill anyone, sure, but it won't be pleasant if he decides to attack. Same for these little yapping dogs.
Now, the rant on dog education. It's common to have this type of problem with toy breeds. People treat them like babies or toys, but they are pack carnivores. So they end up being the alpha animal after a while. And everyone goes "aw, how cute the little dog being brave"... Idiots, Chirac's household included.
Oh, and in case you don't know it can work with cats too. Mine is quite obedient, at least when I am around (I know he does the forbidden things like go on top of the table when I'm not, but that at least shows he knows who's the alpha animal in the house). My girlfriend, that would be. :-)