In deference to David, it cannot be said that aluminum provides absolutely no protection. However, at roughly 1/5 the density of lead, the difference between aluminum and nothing is not readily measurable.
Aluminum foil may not protect you from cosmic rays, but if you make it into a hat, you can probably find lots of room for yourself on the bus.
“Photography is a complex and fluid medium, and its many factors are not applied in simple sequence. Rather, the process may be likened to the art of the juggler in keeping many balls in the air at one time!”
Ansel Adams, from the introduction to The Negative - The New Ansel Adams Photography Series / Book 2
Here's an earlier thread I had about issues with frozen film. I eventually had the negatives sent to Ilford for examination. The exact cause remains "inconclusive", however the best explanation was that freezing/defrosting - ie moisture - was the only likely potential cause. Since this issue first raised its head, I have witnessed enough of the problem that I would say that 35mm film shouldn't be frozen in its plastic canister ONLY - Im trashing all my film stored this way as its too unpredicable. Other rolls purchased at the same time and having gone through the same identical treatment, but remained in their cellophane and cardboard packaging of bricks of 10, appear to be fine.
"Cosmic rays" are not electromagnetic radiation but particles. The higher energy ones pass through the entire planet, so a piece of sandwich foil really isn't going to help very much. The underground vaults mentioned also have a very constant temperature and humidity which probably reduces storage costs considerably.