In the case of the OP, from what she said, it sounds like she did not live or earn any income in Canada or from Canadian sources (like Canadian-issued securities) at all in 2009. I don't think she qualifies as resident in Canada for tax purposes.
You are right that the actual definition of residency for tax purposes comes from the relevant bilateral tax treaty (where such a treaty exists). You are also right that technically, the CRA does consider an individual's worldwide income in determining their tax liability. This is mainly because Canada has a progressive system of individual income taxation. If I earn $50,000 in Canada and $50,000 in a flat tax jurisdiction such as Latvia, the CRA cares about my foreign income for the purposes of determining the appropriate graduated tax rates to apply to my Canadian income. The Latvian tax authority doesn't care so much since they supposedly collect the same amount of tax on every dollar (or local currency equivalent) earned there.
Ultimately, the system of bilateral tax treaties is meant to stop multiple tax authorities from levying tax on the same income. In the example I mentioned, the CRA can only collect tax on $50,000 of income, and not on the full $100,000. If they did, I could apply for relief from double taxation under the mutual agreement procedure article of the tax treaty. The CRA and the Latvian tax authority would then have to work it out.
This example is ridiculous since the amount of tax at stake is so small, but it is an example of how the system works.