Does a 90 year old with a displaced, slightly fractured tibia have to have surgery or can it be put in a cast?

Possibly: Depending on the patient's medical condition, and preinjury walking status, and the exact nature of the fracture (i.e. how displaced is the fracture?), a minimally displaced fracture often can be treated without surgery (i.e. a cast). However, the final decision will depend on the exact imaging findings and the opinion of your orthopedist.