My understanding from my numerous father and son chats on the subject (me dod was in the field) is that ‘fallout’ is irradiated particles of dust and bomb parts which were irradiated by the burst of a nuclear weapon.
They can be washed off sealed food or liquid containers and the contents consumed safely because they don’t in turn irradiate non-radioactive substances, though they do emit harmful radiation as long as they are in contact or close proximity with living organisms.
Here’s a conundrum for ye that me dod gave me as a research assignment once.
Everyone knows that when a nuclear bomb is unleashed on a city it leaves an irradiated nuclear wasteland that makes the city uninhabitable for hundreds of years.
Yet Hiroshima and Nagasaki are today habitable cities with no restricted irradiated zones anywhere, including grounds zero.