[SalesForce] Where does “add team member” button on opportunity team render

Opportunity Team Members cannot be created unless you are the owner of the Opportunity or are above the role hierarchy.

However, there are two ways you can achieve this:

1) Create a Visual force page and then have the logic to add/delete Team Members

2) Create a custom object and write a trigger on the custom object to add team members. Since triggers run on system context, it will create the team member.

Hope it helped.

As some of the cases failed to trigger the Apex Trigger, I did found little mentioning of why they are failing. This Article mentions:

Validation rules and Apex triggers aren’t supported when a user adds his or her default opportunity team on an opportunity.

What else I found out is that even the Process Builders failed to get the trigger along with Apex Trigger in a case when I try to -

“Add Default Team” on the Opportunity team related list in Opportunity view layout

“Add Account Team” on the Opportunity team related list in Opportunity view layout

Additionally, I logged a case with Salesforce to get an Official statement from them.