You can base the visibility of an attribute in an RCDC off of a boolean attribute by binding it to the my:Visible property:

<my:Control my:Name="PositionRef" my:TypeName="UocIdentityPicker" my:Caption="Position Reference" my:Description="%SYMBOL_PositionRefDescription_END%"my:Hint="%SYMBOL_PositionRefHint_END%" 
my:Visible="{Binding Source=object, Path=IsInChris21, Mode=TwoWay}"

Is it possible to set this using the inverse of the attribute instead? In other words, when it's true, to hide a control instead? 

On discussion with some other implementers and based on the response here, I gather it can only be done by populating another field with the inverse of this field, or to use some sort of set-based approach limiting permissions.