Comments - GRANT
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I consider the description of the TRIGGER-privilege to be misleading: The passage "Execute triggers associated to tables you update, execute the CREATE TRIGGER, DROP TRIGGER, and SHOW CREATE TRIGGER statements." could be understand in that direction, that without this privilege, triggers aren't fired when data manipulation is taking place on tables that a user has INSERT, UPDATE or DELETE privilege. This made me somewhat anxious because you'd either had to give users also the right to manipulate triggers to have them executed or WITHOUT this privilege triggers aren't fired and the integrity of the data would be in jeopardy. -- Having tested this I can say: This is obviously NOT, what the documentation text means - triggers are firing ALSO WITHOUT the TRIGGER privilege.
Note that the trigger has a definer. It's the definer, not the invoker, that must have the TRIGGER privilege for the trigger to be executed.