Quote: This doesn't sound very logical to me; does it really make sense to you?
Babies are deformed because something interferes with normal development. They might inherit abnormal genes from their parents which don't code for proper development, or there may be something in the environment (some toxin, for example) that causes a change in the way they grow. Neither is involved when a doe splits a litter and carries two separate pregnancies, so why should the babies be deformed?
It is possible that the second litter might get born at the same time as the first litter. If there is more than a couple of days' difference in the gestational age of the litters, that means the second litter would be premature. Those would be normal (not deformed) babies, just born too soon (I have seen does deliver babies prematurely just from stress a couple of times). Simply having two litters of different gestational ages wouldn't cause a doe to deliver both litters prematurely.
Carrying two litters, or even one large litter, will not by itself kill a healthy doe. If a doe is properly fed and maintained at a healthy weight, pregnancy is only a moderate strain on her. A doe that has been allowed to get too fat may have metabolic issues that could kill her, but that is the fault of the owner, not the pregnancy. A doe that gets bred too often may have her mineral and fat stores depleted to the point that she can't stand the strain, but once again, it isn't the pregnancy itself that is the issue.
I have at times bred by the colony method - putting a buck in with several older does and pulling the does out when they show signs that they were pregnant. Though I have many times heard that it is possible for a doe to conceive two separate litters like this, I have never once seen any evidence of it happening. In almost 30 years of breeding rabbits, I have had exactly one doe deliver babies on one day, and then some more a few days later, but that doe was bred to a buck on one day only. I have had does give birth to what looked like premature babies, but once again, those does were only bred on one day. So while I think it is good to be aware that does supposedly can conceive two litters at once, I think it is very unusual for it to happen.