That can still happen, but it is the radioactive beef from the cows that ate radioactive rice hay that have brought radiation everywhere in Japan.
Now, in the latest tally by NHK, at least 1,698 cows may have eaten the rice hay with high level of radioactive cesium, and they have been shipped and sold in every prefecture in Japan except Okinawa.
An increasing number of Japanese don't believe it's just about the rice hay and the cows, although the government has been trying its best to focus people's attention to them.
(And where there's cesium, there's strontium, as the Nuclear Safety Commission said in early June, when the Ministry of Education announced the discovery of strontium 62 kilometers from Fukushima I Nuke Plant in April and May.)
From NHK News Japanese (4:55AM JST 7/23/2011):
ＮＨＫのまとめによりますと、放射性セシウムを含んだ疑いのある稲わらを肉牛に与えていた畜産農家は、▽宮城県で３６戸、▽福島県で２５戸、▽新潟県で １５戸、▽岩手県で１２戸、▽山形県、秋田県、岐阜県でそれぞれ６戸、▽群馬県と埼玉県でそれぞれ２戸、それに▽北海道と茨城県、栃木県、静岡県、三重 県、島根県でそれぞれ１戸で、１５の県の合わせて１１６戸に上っています。また、こうした農家から出荷された肉牛は、少なくとも１６９７頭に上り、流通先 は沖縄県を除く４６都道府県に広がっています。
According to NHK's tally, the number of cattle farms: 36 in Miyagi; 25 in Fukushima; 15 in Niigata; 12 in Iwate; 6 in Yamagata; 6 in Akita; 6 in Gifu; 2 in Gunma; 2 in Saitama; and 1 each in Hokkaido, Ibaraki, Tochigi, Shizuoka, Mie, and Shimane. Total of 116 cattle farms in 15 prefectures shipped at least 1,697 cows to 46 prefectures, expect to Okinawa.
By the way, Okinawa Prefecture does not have a nuclear power plant, and has received hardly any radioactive plume from Fukushima I Nuke Plant as far as I've seen in the radiation dispersion forecasts by European meteorological institutes. Clean air, clean water, good food. (Well, until those nuclear reactors in Taiwan start to break down in a big earthquake there...)