Citizenship has absolutely no bearing on the provision of benefits under the Old Age Security Act specifically. Here we're dealing with provisions, so I'm going to give you an example.
Let's say someone who is a Canadian citizen happens to move to China. We don't have a social security agreement with China, so that individual would not be entitled to receive prorated GIS benefits. If that person moves back to Canada, they need ten years of residency to open up the right.
This provision is for those people who benefit. By having a social security agreement with another country, it opens up the right for non-sponsored immigrants from those countries to receive income-tested benefits but for sponsored immigrants to not receive them. It's because of the obligation of the sponsor. You could have Canadian citizens, for example, who wouldn't meet the ten-year residency requirement and would therefore not be entitled to GIS benefits.