If you look at Alcoa's specs, the difference in the alloys isn't just magnesium content. [1] See chromium, for example, which is in the alloy for the top but not the body. Besides, even if you can make the body out of the resulting alloy, you can't make the top.
[1] https://www.alcoa.com/mill_products/catalog/pdf/China_Specs/...
Your wikipedia article says:
> When recycled without other metals being mixed in, the can–lid combination is perfect for producing new stock for the main part of the can—the loss of magnesium during melting is made up for by the high magnesium content of the lid.