pt-online-schema-change's triggers fail with "DELETE command denied" on insert

We recently tried pt-online-schema-change to add a column to a table. It worked mostly as expected but one thing puzzles me: in case the account we use to do the migration doesn't have the DELETE permission, our application (which keeps running simultaneously) gets errors that say "DELETE command denied to user 'pt'@'localhost' for table '_xxx_new'" when the app is performing an **insert** on the *xxx* table. My understanding is that the triggers are to do **inserts** to the destitation *_xxx_new* table when a new record is inserted in the source *xxx* table. How come it may fail with not having a DELETE permission?? Percona docs are pretty generic on this and no googling helped, so will be thankful for any ideas!