I read an article yesterday in a European paper, that out of 30 millions aliens living in the US, close to 10 millions were illegal.

It seems that many people come sporadically to work for a season and return home. Some of them are supposed to come from Visa Waiver countries and they were giving an example of a fisher who had been working as a waiter for more than 20 years at the rate of 6 months a year... This particular individual had been caught twice and duly deported. This did not deter him from coming back as a tourist and continue to work. It was further mentioned that the individual is Irish and does enter the US at airports and not over the "green border". Is that possible at all? Especially since the fingerprinting and added security? Or is this just some propaganda?

There is some truth in this -- but it's increasingly less true than it used to be in the past. A fair amount of migrant farm labors do go back off-season, but over the past two decades or so they have been gravitating toward other jobs in the US and not heading back in the same volumes as in years past. Also with the perception that US border security is only going to increase crackdowns at the border, the risk for illegal immigrants to leave and come back is perceived to have gone up; as a result, they don't go back as often and in the same percentages as in the past.

The part that sounds to be not true in the article you mentioned is that he flies into the US even after being deported for immigration violations. He must have been changing his passport since a rejection should have come up even under the older processes.