Used mainly in the US, 'complected' can be unfamiliar to speakers from other English-speaking countries. He mentioned how fair-complected she was, and our British friend seemed confused.
Pro Tip 2/3
Sensitive Contexts
Discussing skin color can be sensitive; use 'complected' with care and respect for diversity. The artist admired how the light-complected girl's skin contrasted with the dark background.
Pro Tip 3/3
Avoid Stereotyping
Don't make assumptions about a person based on being 'fair-complected' or 'dark-complected.' Just because she's dark-complected doesn't mean she's not from around here.