I agree with Jottlebot. There is a BIG difference between air being circulated and drafts.
For example, running ANY household fan just circulates the air in the room.
I always have fans on (I have stand fans and desk fans) and on those hot summer days, your bird may like to breeze from the fan to cool off.
Now a cold draft from an open window or door is another story. Those are the dangers. For example, having a cold draft in the middle of winter when your home is nice and toasty is not good.
That being said, the healthier your bird is, the less likely they are to get sick by any 'cold draft'. Not that I would ever risk it, but I'm just saying a poorly fed bird is much more likely to get sick from a draft.
I even run the AC in the summer with Skittles loose. I just don't allow him to be directly in front of it or its line of air (I have it blow in a direction Skittles doesn't go near).