I'm not attacking you. You argued that you shouldn't believe distances on maps that you haven't personally verified. And I am arguing that there are many facts, such as the chemical composition of the water molecule, that very few of us are able to verify for ourselves, yet we believe these facts anyway.
I will answer your specific question about map distances next, but I think the more fundamental question in my first paragraph above is an interesting one, and it directly relates to your more specific question.