Whether you need to pay taxes in Canada has nothing to do with your citizenship. Regardless of whether you are a Canadian citizen, if you are not a tax resident in Canada, you only pay taxes to Canada on your Canadian-source earnings.
A lot of people get confused between residence and citizenship. The only 2 countries in the world that tax their citizens abroad are the United States and Eritrea. I don't know why so many people in Canada get so confused about it? Maybe it's the influence from the Quebec French language, which does not differentiate between residents and citizens (both of which they call "citoyens")
It's not called a tax amnesty, it's a treaty to avoid double taxation. It's based on the principle that taxes should only be paid once on the same income, not on forgiveness. They are useful to you in 2 situations: 1. You are a resident of Canada and earned income abroad. 2. You are not a resident of Canada and earned income in Canada. In both of these cases, you get a credit in Canada for all taxes paid abroad in treaty countries.
If and what return you need to file in Canada is determined by whether you are a factual resident, deemed resident or non-resident of Canada for the tax year. If you spent most of the tax year outside Canada, you can only be a deemed resident or a non-resident. If you maintain sufficient ties to Canada, you file a deemed resident return with Canada (no provincial taxes). If you have no ties (no car, house, driver's license, other significant property) left in Canada, you are a factual non-resident of Canada and then you have to file a non-resident return only if you had any source income in Canada. If you file in the wrong category, they can reassess you in the proper one, regardless of citizenship.
Summed up, a tax return is not the place to prove your citizenship (attempting so may be grounds for a fine). You maintain citizenship in Canada regardless of whether you filled an income tax return, except if you explicitly renounced citizenship. To prove your citizenship, you need to keep your birth certificate or citizenship certificate in a safe place.