When you add Canadian to the list of citizenships you hold, the ETA form rejects you out of hand. You don't even get to submit the application. Interestingly, the error message does not mention the "special authorization".
Yeah, that's a much simpler check, assuming a person honestly discloses they are a Canadian citizen the eTA form doesn't allow it to proceed.
What I was referencing earlier is the system checks on completed eTA forms. When someone "
appears to be a citizen of Canada" the system will drop a completed eTA application out of automatic processing for a check by a human being. But the earlier post I linked to indicates that this check only works if the citizen is naturalized.
Basically:
1) If you put that you're Canadian on the eTA form, the form blocks you from proceeding and tells you that you can't.
2) If you don't put down your Canadian citizenship on the eTA form but you naturalized, the eTA application flow can reconcile your biographical info against the records showing you were naturalized and your application is dropped out of automatic processing.
3) If you don't put down your Canadian citizenship on the eTA form and you gained citizenship by birth in Canada, then the eTA form cannot automatically reconcile that you are a Canadian citizen (even if you hold a valid Canadian passport) and it would process automatically unless there was a block on your eTA for some other reason.
The situation where someone who is a Canadian citizen is probably pretty niche. If someone was aware of the loophole and wanted to just apply for an ETA for whatever reason (maybe they didn't want to bother with the hassle/expense of getting a Canadian passport when already having a passport from a second citizenship) that's one. Or maybe in certain cases the person is not aware that they are considered a Canadian citizen, perhaps due to changes in the Citizenship Act they were not citizens before and are now considered citizens, or maybe they lived most of their lives in a foreign locale and they are somehow unaware of jus soli citizenship.