If someone is prescribed glivec, does this mean they have cancer?

Usually - yes.: Gleevac is used for the treatment of various cancers, including Philadelphia chromosome positive chronic myelogenous leukemia (CML), some cases of Ph+ acute lymphoblastic leukemia (ALL), gastrointestinal stromal tumors (GIST), or rare cancers like mastocytosis. Other 'pre-cancer' diseases (some myelodysplastic syndromes) and non-cancerous hyper eosinophilia syndrome can be treated with Gleevac.