The office of the Headmaster or Headmistress is located high in a tower overlooking the grounds and providing a vista of the mountains beyond. Access to the office is by means of a magically moving spiral staircase on the seventh floor (HBP), although perhaps this entrance moves around since Harry found it on the second floor on one occasion (GF28) and on the fifth floor on another (CS11).
The entrance with its gargoyle and revolving staircase is clearly located on the seventh floor all though HBP. However, on one occasion in GF28 Harry finds the entrance on the second floor. In the second book, the entrance seems to be a floor above the library, which we know to be on the Fourth Floor (CS11). This is one of the few examples in canon of a location in the castle changing between books. As a "within the story" explanation, we might say that the entrance manifest itself on a nearby floor because it senses the urgency of the situation. This fits with evidence all through canon of magic adapting to the intent of the caster (such as Expelliarmus hurling someone across the room when the caster is particularly angry with the target).
Note that the statue guarding the entrance to the Head's Office is not a Griffin as shown in the films. The door knocker to the office itself is a Griffin, it's true, but the statue to which one states the password is a gargoyle.
They marched in silence around a corner and she stopped before a large and extremely ugly stone gargoyle.
"Sherbet lemon!" she said. This was evidently a password, because the gargoyle sprang suddenly to life and hopped aside as the wall behind him split in two. Even full of dread for what was coming, Harry couldn't fail to be amazed. Behind the wall was a spiral staircase that was moving smoothly upward, like an escalator (CS11).
So this meme, while cool as a film easter egg, is not accurate according to canon.