How do I resolve this denied permissions error?

No, you need to fix the roles and permissions.

So far, in my 10years of experience, most of the users claiming the permissions are correct when permission errors occur did some kind of misconfiguration or did not understand how roles and permissions work.

You can, maybe, prove me wrong if you provide useful information supporting your claim.

Back to your question, make sure the user has a role that allows him to save the work item in the target state in the context the work item lives.

To update on this issue:

Users (in the same project area) are receiving this error when creating a new work item from a plan view. They are able to create work items from Work Items>Create Work Item>WI Type and link them to the plan.

We recently upgraded from Rational Tools 6.0.2 to 6.0.4. The users were able to create work items from the plan view prior to the upgrade. No permissions have been changed since the upgrade. I have compared all settings in the live environment to the settings in the test environment (same version of Rational Tools). Using a test account with the same permissions as users, I am able to successfully create a work item from the plan view in the test environment, but am not able to do so with the same account in the live environment.