Sending an email to a task (including milestones) follows the same permissions required to log into the interface and write a comment:
Since Administrators can see all projects so they are not bound by project permissions. All other user levels (Manager, Resource and Executive) need to be part of the team for the project that the task belongs to.
If they are an Executive, they need to have the permission “Allow commenting on tasks & milestones” to be enabled in their profile.
For an in-depth look into email integration with Intervals check out The Request Queue, Hopper & Email Integration Video below: