harry potter - Are werewolves in the Forbidden Forest consistent with later explanations on werewolves?

In the Philosopher's Stone, Harry, Hermione, Neville and Draco are punished and have to assist Hagrid in his search for a dying unicorn.

Malfoy mentions that according to rumors, there are werewolves in the Forbidden Forest. When they ask if a werewolf could kill a unicorn, Hagrid answers that they are not fast enough to do that. He does not answer, "There are no werewolves in the forest", which is evidence that there are indeed werewolves (since Hagrid knows the ins and outs of the Forest as we are told).

Now from what we learn in The Prisoner of Azkaban, werewolves are humans that were bitten by other werewolves; they transform into werewolves during a full moon.

Does the information we get on werewolves in book 3 contradict what we can infer from book 1?

In particular:

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  Why would Hagrid not refute the idea of werewolves attacking unicorns simply using the fact that they transform once per month, and that Hagrid found two different unicorns attacked in a week (instead of using a dubious speed argument)?

  
  


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  Why would werewolves stay in the Forbidden Forest all year, when we know werewolves are actually human people who, although they are often rejected by normal wizards, would probably not be ignored by Hagrid and especially by Dumbledore, who I can't imagine would not offer any help to infected people staying in the forest near his school.

  
  


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  Why would they even let werewolves occupy the forest if one bite on a student could kill him or infect him for life? Sure it's the "Forbidden" Forest but, assuming there were werewolves as described in book 3 in it, the werewolves would probably drastically decrease the security of students.

  
  

Answer

The "Werewolves" in the Forest are Actually Highly Intelligent Regular Wolves

This is from the Pottermore entry on werewolves:

One curious feature of the condition is that if two werewolves meet and mate at the full moon (a highly unlikely contingency which is known to have occurred only twice) the result of the mating will be wolf cubs which resemble true wolves in everything except their abnormally high intelligence. They are not more aggressive than normal wolves and do not single out humans for attack. Such a litter was once set free, under conditions of extreme secrecy, in the Forbidden Forest at Hogwarts, with the kind permission of Albus Dumbledore. The cubs grew into beautiful and unusually intelligent wolves and some of them live there still, which has given rise to the stories about ‘werewolves’ in the Forest – stories none of the teachers, or the gamekeeper, has done much to dispel because keeping students out of the Forest is, in their view, highly desirable.

So the wolves in the Forbidden Forest are the product of two werewolves mating during the full moon. They are wolves all the time. They aren't particularly dangerous -- certainly not as dangerous as werewolves during the full moon. And even if there is some mild danger associated with them, this isn't inconsistent with the books since lots of things in the Forest could be dangerous -- the gazillion giant spiders that are only kept in check by Hagrid and Aragog, for example.