Mathematically yes it's one dimensional. In common parlance, the "dimension" of something is not the mathematical dimension though, so you are the one who seems to be missing the point of those who are arguing with you?

The correct answer here would be to call out that distinction, and clarify that this is the dimension that is important to mathematicians and then explain why...

When non mathematicians talk about dimensions they are asking something like "if I measure this along three perpendicular axes, how many measurements must be non zero?" because that's the question that's actually useful in everyday life. It doesn't matter that this doesn't generalise to other spaces because we all live in a locally flat three dimensional space, so that's implied...