It is unlikely that the mother could give birth to six fused kittens her birth canal simply could not accommodate them. Conjoined individuals originate from a single egg. This means the kittens should have been identical sextuplets and all the same colour and same gender. I therefore find it unlikely that they were born conjoined.
It is more likely that they became stuck together after birth. Similar things have been seen in so-called rat kings or squirrel kings where the newborns become glued together by blood, amniotic fluid, tangled umbilical cords, excrement etc, or by tangled tails. Tangled kittens not unknown where the mother cat is inexperienced or cannot cope (or has given birth in wet, dirty surroundings).
Sarah Hartwell, Feline Medical Curiosities, at http://www.messybeast.com/freak-cats.htm.
Animal-lovers and freakshow enthusiasts everywhere are grieving after the death of Mishka, a Siamese Siamese cat that was joined at the head to its sibling Mou-Mou. Surgeons in Moscows Laika Veterinary Hospital had been confident that one of them would survive the separation process, and attempted to save Mishka after CNNNN's studio audience determined she was more worthy of being spared. But as luck would have it, Mishka ultimately perished on the operating table. Mou-Mou pulled through, albeit with only 10% brain function.
CNNNN commentator Chris Taylor, who was very close to the pair he called his special Siamese Siamese pals, observed isnt life funny sometimes? The death of Mishka plunges into uncertainty their bestselling range of Siamese Siamese cat accessories in Russia. Fans had eagerly snapped up the pair's special conjoined feeding bowls and tins of conjoined cat food. Mishka will be buried in a pet cemetery in the outskirts of the Russian capital. It's expected that when Mou-Mou passes away, she will be buried in the same plot, which will be marked with a specially designed conjoined headstone.
One Siamese Siamese cat dies after separation ordeal, CNNNN, 28 Aug 2003.