I actually disagree with the headline of this story.

There are parts of the river that are polluted after heavy rain (and in some urban areas all the time), but the majority of the Hudson River in rural areas, is now safe for swimming year around. The water quality generally is good along long rural sections of the river, it's mostly an urban sewer overflow issue.

There are actually several public swimming beaches on the Hudson River, including the Ulster Landing County Park in Kingston.

http://ulstercountyny.gov/public-works/ulster-landing-county-park