that they have never lost an appeal as they are full
From Y3, the school can legally take more children than 30/class.
If the school is 'full' in the sense of the PAN having been reached, the application is denied (by the admissions authority, which can be the LA or the governing board) and the parents go to appeal. In the appeal the parents have to argue that the detriment to their child in not attending this particular school is worse than the detriment to the school in taking one additional child.
So if a school has very generous buildings with large classrooms, some extra spaces/rooms, etc then it is easier for the parent to argue that the detriment to the school in taking one additional child is small, and the school might lose the appeal/the parents might win it.
However what your head might have been saying is that they do not lose appeals for this reason. They are 'full' i.e. with the given number of children, there is simply no space left. For example, the classrooms are tight and there wouldn't be space to fit in an extra desk and chair without breaching fire safety regulations.
So if a school is 'full', not in the sense that it has reached its PAN, but in the sense that it cannot fit more children in safely; then it is very hard to win an appeal. The detriment to the school would be huge if it were forced to admit an extra child; so this will only happen if the detriment to the child to not go to this particular school was even huger.
This has little to do with PAN and everything to do with the actual size of the buildings/facilities. Schools that are 'full to PAN' can and do lose appeals; schools that have 'full classrooms' would not often do so.