Privileged Function Access Issue

Summary

Trying to get Privileged Function to Create Record on custom Object

Content

We have a custom Object which is populated by trigger when an Activity Record is deleted.

Which Calls the Following Object Function running as Privileged

We have provided the Privileged Role access to the Custom Object

But when the Trigger fires we get the following Error

I am at a loss as to why the issue is occurring as the Privileged Script Administration has Create access to the Object?