Why is it a manager can't or doesn't have access to give a customer a district managers contact info? To make a complaint.

Because they don't want you to have it

Complaints are to be directed to the hotline. Corporate then contacts the appropriate staff to handle the complaint at the store or district managerial level

Because there's no reason to be a turd and bother their boss when there is a easy to use hotline specifically for complaints

Because there is a manager there between 7 a.m. and 2 p.m.