People living in countries remote from the Soviet Union have certainly contracted cancer and died because of Chernobyl. The Senate's motivation, like that of many political acts, is hard to determine. One commentator compared the Republican party to Wile E. Coyote running off the cliff in pursuit of the Roadrunner. The explanation offered by the Republicans themselves was that the treaty was flawed and that it is not always possible to verify testing. If the Senators sincerely believed the treaty was flawed, they could have exercised leadership by sending the President back to the bargaining table to obtain some improvements to it.
Any businessman knows that an authority-responsibility split is a bad thing.
It is typically manifested in the common spectacle of a hapless middle manager, responsible for a task but lacking any authority to accomplish it.