Field and Form Rules - fail when user submits incident/request

Field and Form Rules - fail when user submits incident/request

We are looking to combine several Incident Templates into a single template by asking the user to select which system they are having issues with.  Once they submit it we want the group to be assigned according to their selection.  The problem we have is that the Field and Form Rules don't work if the requester doesn't have access to the group field when they fill out the template.  Is there any way to fix this?  Adjust a Role?

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