Yes there was exposure, certainly those 4000 children recieved high enough levels. However this is a far cry of hundreds of thousands of dangerous exposures, massive increases of cancer rates and birth defects that are still happening that most people think of.
I myself thought just that until recently after investigating it.
I was studying in Russia when Chernobyl occurred, and I dated a woman from northern Ukraine who was a teenager at the time of the accident. I saw the results of the accident firsthand - basically everyone under the age of 10 was affected - hair loss, skin rashes and nausea in the immediate years after, cancer and early death later.
But even so it isn't fair to judge the safety of nuclear power by Chernobyl. Chernobyl happened because the Soviet system had become incredibly incompetent, and technical decisions were being made by thugs.
The capitalist system quite often also becomes incredibly incompetent and has its technical decisions made by thugs. Tepco, the company that runs the Fukushima plant, has a long history of corruption, faked security reports and blatant incompetence.
What makes nuclear power unsafe is human error more than technical failure. That's the aspect the naive technocrats (like the guy who wrote this article) always ignore.
"Models predict that by 2065 about 16,000 (95% UI 3,400–72,000) cases of thyroid cancer and 25,000 (95% UI 11,000–59,000) cases of other cancers may be expected due to radiation from the accident, whereas several hundred million cancer cases are expected from other causes. Although these estimates are subject to considerable uncertainty, they provide an indication of the order of magnitude of the possible impact of the Chernobyl accident. It is unlikely that the cancer burden from the largest radiological accident to date could be detected by monitoring national cancer statistics. Indeed, results of analyses of time trends in cancer incidence and mortality in Europe do not, at present, indicate any increase in cancer rates—other than of thyroid cancer in the most contaminated regions—that can be clearly attributed to radiation from the Chernobyl accident."
What SOME reports are saying. You are cherry picking the lowest counts.
"But other reputable scientists researching the most radiation-contaminated areas of Russia, Belarus and Ukraine are not convinced. The International Agency for Research on Cancer, another UN agency, predicts 16,000 deaths from Chernobyl; an assessment by the Russian academy of sciences says there have been 60,000 deaths so far in Russia and an estimated 140,000 in Ukraine and Belarus.
Meanwhile, the Belarus national academy of sciences estimates 93,000 deaths so far and 270,000 cancers, and the Ukrainian national commission for radiation protection calculates 500,000 deaths so far."
I myself thought just that until recently after investigating it.