doesn't it depend where the fire starts?

'Burn down' would refer to a structure that has been destroyed by fire:

• The house burnt down.
• London Bridge is burning down.

'Burn up" is used in special ways, usually to do with science and substances:

• The meteor burned up as it entered the atmosphere.
• Running 10K burns up a lot of calories.
• Driving that fast burns up gallons of gasoline.

True story, my house caught on fire and the patio, living room and 1-1/2 bedrooms the roof as well as part of my face, hands and feet were burned up, and while I was trying to put it out, save my daughter and four dogs, half of my house burned down. Still confused? Maybe it will make more sense when it happens to you.

It really comes down to the fact that the words "up" and "down" have several definitions and some of those definitions crisscross each other, meaning you can get tied up or tied down trying to understand it. If the house is happy, then it will burn up, but if the house is sad, it will burn down. Unless the house is sad, but still headed toward a happier place, then it will burn up.