Just for clarification not sure I understand the above given in the ETA application there is a specific question on any additional nationalities the applicant may hold. So are you saying that even if someone who holds a visa exempt passport puts Canada in answer to this question as they were born in Canada but are somehow dual citizens they will still get an ETA even when the application reaches the ETA review/issue stage.
While the PDIs state (in multiple locations) that a "Canadian citizen" is not eligible for an eTA, almost all eTA applications are processed automatically, no human processing agent sees let alone examines the eTA application unless it
drops out of the automated process.
Here (with some emphasis added) is what it says about Canadian citizens applying for eTA under procedures in one of the PDIs:
"In some cases, applications can drop out of the automated process because the individual appears to be a citizen of Canada. The system will catch such cases only if the individual is a naturalized citizen; individuals who are Canadian citizens by birth will not have a record of their citizenship in GCMS and will therefore not be identifiable by the system."
I am not familiar with the particulars of the application. If the prospective traveler must disclose additional nationalities, and discloses "Canada," I do not know how the system responds. If the prospective traveler discloses Canada as an additional nationality, and the system thus drops the eTA application from the automated process, it is manually processed. If that happens, the prospective traveler should be informed a Canadian citizen is not eligible for eTA, that their eTA application has been withdrawn, and the individual must use their Canadian travel document to enter Canada.
But the language in the PDI suggests this will not happen unless the eTA applicant is a naturalized citizen with a record in GCMS, and thus identified in the system as such. Indeed, the PDI procedure further instructs the officer to consider, based on "case history" (which is accessible only in the GCMS) if the individual has been
granted Canadian citizenship, or is appearing as a citizen in the system but that citizenship has been revoked (there is no process for revoking citizenship obtained by birth). It virtually ignores or does not address a scenario in which the eTA applicant appears to be a citizen by birth, other than to note that such citizens are not identifiable as Canadian citizens in the system.
So I do not know the answer to your question. But it is apparent the system is not designed to enforce the Travel Document rules as strictly or diligently for citizens by birth as it is for naturalized citizens.
Is this a bug or a feature? as the software guys might phrase it.
Of course, for decades the travel document requirements were unequally enforced against PRs who were not from a visa-exempt country compared to those PRs carrying a visa-exempt passport. So such disparities are not unusual.