Yes, you're right about the humidity being the biggest factor, and that will also make bread go stale. It also depends on whether it's prepackaged bread or freshly baked. Prepackaged bread is less likely to arrive with mold spores, and the packaging keeps humidity out during transit and storage. Once it is opened to the humidity, especially in tropical climates, refrigeration will slow any growth.

For people in arid climates, their refrigerator might actually be more humid than their cupboards.