I disagree with the above advice (as an employee, you should never ever state the number first), however I think the assumption behind this advice would be that

I disagree with the above advice (as an employee, you should never ever state the number first), however I think the assumption behind this advice would be that you the company believes it's competing against other companies for you. So, they wouldn't do the lowest because they want to outbid the competition, and the higher number acts as an anchor. But again, as a candidate, never say the number first.