You understand wrong. 25% of Republicans voted for Orly.
If you are unaffiliated with any party ("decline to state" or "independent"),
•You may request the ballot of the Democratic or Republican Party at the polls on June 8, 2010 or on your vote-by-mail ballot request form, or
•You will be given a nonpartisan ballot, containing only the names of all candidates for nonpartisan offices and measures to be voted upon at the primary election.