That's not snobbery, it's simple (but understandable) inaccuracy. Most people don't know that "Prof" is a job title, "Dr" is a qualification (specifically a degree). You can be either without the other - I know a Prof without a doctorate.

It's akin to confusing a linguist with a polyglot, a top-level accountant with a research mathematician, or someone who writes HTML with someone who programs in Python. They are simply different. Not getting it right is either a mistake, or a demonstration of lack of knowledge of the difference.

EDIT: Added the first parenthetical clause.