A good question, Guest.
The explanation lies in the fact that the Allocation Profile is published in March, whilst these figures are the actual take up of places in September. A lot can happen in 6 months!
Two schools fall into the category you describe - AGS with one spare place, and Burnham GS with 47 places. (The remaining schools that still have places were "All Offered" on the Allocation Profile.)
Burnham illustrates the issue best. In March Bucks were only able to offer places up to a certain distance because they had more applications than places. However, many applicants did not take up their places because they had passed the entrance exam for one of the Berks Grammars. Therefore, by September, all applicants had been offered places and there were vacant places left over.
Burnham is an extreme case because it is (allegedly) one of the weakest Grammars in Bucks and it is so close to the County border.
In the case of AGS the 1 spare place is probably just a few people deciding to go elsewhere over the course of 6 months.