From Kodak:
Ambient gamma radiation is composed of two sources: a low energy component which arises from the decay of radionuclides and a high energy component which is the product of the interaction of cosmic rays with the earth's upper atmosphere. The radionuclides responsible for the low-energy photons exist in soil and rock and are carried into earth derived building materials such as concrete. Lead shielding or storage deep underground may be helpful, but for long-term raw stock storage, radiation will still be a factor. Upon exposure to ambient-background radiation, photographic materials can exhibit an increase in minimum density, a loss in contrast and speed in the toe, and an increase in granularity.
The change in film performance is determined by several factors, such as the film speed and length of time exposed to the radiation before the film is processed. A film with an Exposure Index (El) of 500 can exhibit about three times the change in performance as a film with an El of 125. While this effect on a film product isn't immediate, we still suggest exposing and processing the film soon after purchase. We recommend a period of no more than six months from the time of film purchase before exposure and processing, provided it has been kept under specified conditions. Films kept for extended periods beyond six months may be affected, especially the faster films, even if they have been frozen. The only way to determine the specific effect of ambient-background radiation is to make actual tests or measurements by placing a detector in the location where the film is stored. The most obvious clue is the observance of increased granularity, especially in the light areas of the scene.
http://www.kodak.com/US/en/motion/support/technical/storage_cond.jhtml#radiation for the original citation.
Don't believe me? Test it for yourself. Buy some slow film and some really fast film. Freeze both for a few years. Shoot and process.
At one time (and perhaps still), Kodak had storage facilities deep underground (in abandoned mines, if memory serves) for film storage. Hundreds of metres of rock stop cosmic rays to some degree (but not completely), so the effects on the film are reduced versus storage near the surface.
A freezer does not stop cosmic rays. Loading the freezer with food does not stop cosmic rays.
It might sound like a joke, but cosmic rays and background radiation have noticeable effects on film, especially faster film, over periods of time that we are likely to care about.