There were extensive public hearings and research into the epidemiology of arsenic in drinking water, including cost-benefit analyses of how much lowering the standard would cost vs. how many cancer cases would be prevented.
If you're REALLY interested, two of the rule-making reports are linked to the Web page below. They are very long. But they show that the Clinton administration didn't pick 10 ppb "out of their booties". They also estimate that for the 10 ppb (or micrograms/liter) standard, the costs of implementation are about the same as the savings due to the reduced number of cancer cases and other health improvements. Look at Table III.E-7 in the "Final Rule" report.