Answered runProcessor

The create processor requires the new_document permission. If the resource will be in the root of the tree, new_document_in_root permission in required, otherwise, add_children permission for the resource parent is required.

The update processor requires save_document permission and sometimes publish_document or unpublish_document.

There's no way I know of to turn off the permission checks in the processor.

If you really want to bypass them, you can create and update the resource directly with $modx->newObject('modResource') and $resource->save(), but the standard create and update System Events won't fire (e.g. OnDocFormSave, OnBeforeDocFormSave), so any plugins that depend on them (e.g., defaultResourceGroup) won't execute.

Another method would be to create your own processors that extend those processors, and override any methods that check for permissions.