With strangers you have no relationship to protect, so the calculation is different from every other level. You're not managing a friendship or a hierarchy. You're managing something Koreans care about intensely in public space: not creating a scene, and not making the other person lose face in front of onlookers. The tool for that is a word so useful that learners often call it the single most valuable thing they picked up in Korea.
Four ways to say it
The rule underneath
Korean refusal at this level works by leaving the refusal unsaid and letting the other person infer it. That inference is the listener's job, and Koreans are trained to do it from childhood — the skill has a name, 눈치. This is why "괜찮아요" is not vague or evasive to a Korean ear: the ambiguity is a courtesy, and reading through it is expected.
It also explains a real hazard in the other direction. If a Korean answers your offer with "괜찮아요," they have probably declined — even though the dictionary says the word means fine. Learners regularly hear it as acceptance and keep going, and then discover they've become the 민폐 in the situation.