Thank you for your response. I was able to edit the "Welcome To DotNetNuke" module. Did you grant this account edit access by assigning "Membership" edit privileges directly to the module? I have found that the problem is only reproducible when an account is granted access via a child portal role. For instance, I should theoretically have problems if you instead remove direct edit access for the "Membership" username, create a test role in the child portal, add "Membership" to that role, and then grant that role edit access to the module.
Additional interesting behavior on this test site is that although "Membership" is able to successfully edit, it seems to be automatically logged out after a successful edit. Could to the two behaviors be related?
Thanks again for your help.