This applies to the Advanced, Professional and Enterprise level plans.
If you are on lower tiered plan, all your users will show up as viewers and they do not have access to edit anything other than their own alerting settings.
There are 3 different access levels in Pingdom, this is selected when a user is invited and can not be edited later by an admin.
Users are added from Users and teams > Users in My Pingdom. All users have their own accounts with at least a free subscription. They can switch the account they are administrating by clicking the box in the lower left corner in My Pingdom
The current options available are:
Can make changes to the account, checks, etc. Including changing subscription information, invite new users and much more.
Can add and edit checks, view reports.
Can view checks, reports.