The Duchy of Cornwall is rather different from Cornwall. Historical Cornwall is much bigger than modern Cornwall and this is one of the many oddities of Cornish nationalism.
I don't think it's down to "perception" so much as archaic laws surrounding royal estates that even royalists aren't too happy about.
This is also true of Welsh nationalism which seems quite content to believe that a thing called Wales has always existed within (or close to) its 1974 borders.
I meant the creation of those archaic exemptions were down to the belief/need to treat "Cornwall" differently.