To confirm, changing that value should be OK and not cause anything to go haywire?
No this will not cause Method to go haywire.
The App Specific column represent the selected Acitivity Type can only be found in a specific application within Method.
Ex. Our "Work Order" activity is only found within our Field Services App. So under this column then the "Work Order" has a 'Yes'
If you change the 'Meeting' activity 'App Specific' column to 'No' then you should see this activity back in your list.