Whether the rabbit/hare or hyrax chew their cuds is irrelevant to finding inaccuracy in this section of the Bible. The Bible says each of these animals is unkosher because "its hoof is not split." Lev. 11:4-5. But, neither of these animals has hooves. Does anybody have a rabbit's hoof for good luck? And the Hebrew word here (Parsah) is not generic; it specifically means hoof, not foot and not paw. Verse 27 later in the chapter uses the term "its paws" (Cahpov), so the use or misuse of language here is very important.
Remember, this section is about kosher and unkosher animals. More to the point, verse 3 focuses on kosher animals that have both split hooves and chew their cuds. Verses 4 through 7 only list those animals that have one, but not the other. Jewish sources say that these are exhaustive lists that prove the existence of God. While that may be a stretch, at the very least these verses should include real examples of unkosher animals that might be mistaken as kosher.
The camel is a great example included here. It chews its cud and has a hoof, just not a completely split, cloven hoof. The pig makes a little sense if there could be a mistake as to what "chewing its cud" actually means. Clearly, there is a lot of debate over hares and rabbits chewing their cuds as opposed to cows. This thread has hyraxes waking up in the middle of the night to chew their cuds, so why not have a fear that pigs do the same? Anyway, let's assume that Jewish bacon lovers needed something in writing to tell them that pigs were off the menu.
That leaves the hare and the hyrax. What in the world are they doing here? They have no hooves. No one reading these verses would have thought that if they saw a monkey chewing gum it was time to get out the barbecue. Even a monkey appearing to chew its cud has no hooves, much less split hooves. Why include a warning for any animal that is clearly unkosher upon visual inspection?
And if a pig needs to be mentioned as a warning, what about a hippopotamus? At least that's a real life example of an animal with split hooves that someone might think is kosher. It's the same suborder as a pig and whether it chews its cud, given its undomesticated environment, might be an open question.
The Rabbis would say that the suborder Suiformes is the same for the hippo and pig. They would point to this as evidence that God exists because only God could have put together a list of all the animals that chew cud but have no cloven hooves or visa versa. Of course, the Jews in the desert knew nothing of suborders or animal classifications that wouldn't exist for thousands of years.
Also, given the lax definition of cud chewing, I'm sure some zoologist could come up with an animal that appears to be chewing its cud for some portion of the day and was not included on the suborders listed in these verses.
But I digress. If God wrote the Bible, and according to the Rabbis, not one letter or dot of the Old Testament is wrong or superfluous, then hares and hyraxes must have hooves. The Hebrew literally says for both that while each chews its cud "its HOOF is not split." It could have said it doesn't have a split hoof, which is technically correct. But God appears to think these animals have hooves.
As stated above, the chapter later uses the word paws, so this is not a case of using a generic term. The animals could have been used as examples of cud eaters who were unkosher without stating that they had no split hooves (which was obvious). From a Jewish perspective, that would have saved several extraneous Hebrew letters; and God could not have put in extra letters. If you delete the hare and hydrax as obvious examples that needn't be mentioned, you save even more letters.
Letters also have a great significance for the Rabbis since they each have a specified numerical value that can help to explain the text and teach other lessons. Extra letters are no small matter, and in this computerized world where the Bible is looked to for codes, they take on an even greater meaning.
Yes, I may have been too skeptical as a yeshiva student. But I have a hard time finding a divine hand in passages about hares and hyraxes with hooves.