So... that's it! Could there be some relation between them that we don't know yet?
I'll point my facts:
1. In the third book Hermione bought Crookshanks. Some say he is a Kneazle. I, myself, believe he is one. So... In Fantastic Beasts and Where to Find Them, under Kneazle, it's said that it is necessary a special authorization to have one. Harry and Ron were outside the pet shop and Harry (and therefore, us) don't know if she was in possetion of such a document.
2. Hermione was using the Time-Turner, and it was McGonagall that made it possible for her to have it.
3. In the fifth book (I think it is the major fact), at the opening cerimony, Hermione, Harry and Ron where sitted in the middle of their table. It was when Umbridge made that stupid speech. After it, Hermione explains that the speech meant the ministry was interfering with Hogwarts.
Some time after that, McGonagal asks Harry if he has listened to Umbridge's speech and, as he says Hermione's explanation. McGonagal then says: 'I'm glad you listen to Hermione Granger at any rate'.
How could she have listened to Hermione if they were very distant?
(Sry for the long post... I hope you understand my point of view...)
Edited to change title