In technical terms this permission is actually briefly called “Write Calendar” which grants write access to a user’s calendar. This is also needed by Pure calendar and Pure grid calendar for adding new events to your calendar.
This bit about “sending emails behind your back” is technically only an implicit consequence of the “Write Calendar” permission and is not and won’t be done by Pure calendar or Pure grid calendar at all. It’s used only when creating events with attendees, it will automatically send them an email. It is not possible to add attendees when creating an event with Pure widgets.