As far as I know, it is not a bug. I guess it makes sense that they share the same timer since you would be able to spam both back-to-back if it were otherwise the case.
I think Blizzard restricted the timers because it would be possible to put too much damage in little time. Therefore, you would probably pull hate from your pet or any other tank.
As it is, I pull hate almost every fight towards the end of it. If I could spam both, I would probably end up with the hate from the beginning to mid-fight, and at least I would not like that to happen.
This is what I think on the matter from what I can see. Maybe some other more experienced Hunter can provide you with another idea or thought.