There is no exemption for monetary rewards earned at the Olympics, or monetary rewards earned elsewhere. Any monetary reward is income to you, and it will be reported on a 1099.
The article is misleading in that it makes the reader believe that the I.R.S. has a standard 35% tax rate for all Olympic monetary rewards; it does not. The example of $3,500 in tax liability on a $10,000 monetary reward assumes a 35% tax rate for the individual.
The only way an Olympian would not be taxed on their rewards is if legislation were passed which allowed an exemption for that type of income.