Q. The sync works great, but users are unable to edit events they did not create from their phones. They can delete events, and add new ones, and they get synched properly, but only the person who created an event can edit it. Is there some specific permission, or is this a limitation of the android calendar application?
 

A. No, nothing specific.  The answer is in the rules of each relationship. Set the relationships TO these users you want to be able to edit destination items and have their changes go back to the source with the following settings:

Conflict resolution:  Overwrite source

Copied resolution: Write changes back to the source

And they will be able to edit them

BTW, Deletion of items are the next two options of the Rules of the relationship.

You don't have to allow users to delete the items if you just want them to be able to edit them, but if you do want them to Delete the Source items if they delete their copies, you can set the rule of the relationship Delete Destination items to Delete Source Items... but be careful who you give that ability to.

The safer way is to allow the owner to be able to delete their items (they always can) or someone you grant permissions to in their relationship or by giving a user client permissions in the public folder, and setting the relationship TO that folder with the permissions above.  In the safer approach, the more "forgiving" approach is to set the rule of Destination Item deleted: to Recopy the item if they delete it or the Do nothing (to the source) option and if their destination item is deleted, it will recopy or not copy back from the Source.

Almost in every case, the rule for Source item deleted is to delete the destination item, but it is also flexible based on your business rule for that type of folder relationship.