Exactly, but that doesn't tell us if you're actually religious or not! You may or may not have a personal religion. That's why I found it weird in this case, where the while point of the survey was to know if people are religious.

It's not clear because secularity usually means the subject - usually an institution - is not tired to a specific religious order (like your definition implies). But unlike institutions, people may have personal religions/religious beliefs, so "secular" doesn't actually tell us if they're religious or not!