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Well, I understand your question. The broadFileSystemAccess could let you access to all files that the user has access to. But it doesn't mean that your app has the admin privileges like your account. When you go the C:\windows\temp in the file explorer, it will ask you to run as admin.
And second, yes, the Store apps needed to be UWP apps. But the snip & sketch app is using FileSavePicker, you could also use FileSavePicker in your app and you could get the same behavior with snip & sketch. Please refer to this document: Save a file with a picker .