I have almost the exact same issue as described here whereby a user receives an error when running a WF that Creates an Item in another Library. The key distinction is my user has the correct permissions I think - He has Edit. If I give him Full Control then he has no issue running the Workflow. Why is this occurring ? Any suggestions ?
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I understood that your user has edit permission on the list in which the item is to be added.
First thing I'd check is that the permission level hasn't been manipulated. If you use default edit permissions I'd check the "Edit" permission level that should have item creation checked:
If thats the case it would be helpful to have a screenshot of the configuration of your item creation action and the permissions on the list.