It does hold water...if you use bicubic interpolation when resizing and don't resize at an odd ratio you will get AA. This is why one of the most obscure but useful feature requests by studios is to be able to animate frame sizes while rendering - it's so high detail scenes that take ages to render at high quality can automatically be rendered at larger resoltions but with lower quality settings then just resized as a post process. Of course resizing down only works as a post process.
You said that you rendered it smaller...that will not work - render large then resize at the compositing stage.

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