So you have both logged in users that can not purchase the ‘discount’ ticket and logged in users that can?
Exactly, I followed your guidance to create a membership site and I assign the ‘um-member’ capability for those who purchase membership. There will still be lots of users who are logged in and can see their past registrations etc, but they will not have access to member prices and activities until they purchase the membership and get assigned the ‘um-member’ capability.
Why is it a mistake?
For a training, one person should only need one ticket, not two. Either the normal ticket, or if the user is a member, then the discounted member ticket.