Iran thought she was a spy because... she decided to lie and tell them she was a spy.

FROM cbs.com and msnbc.com and NPR
Saberi stated that she lied to the Iranian government that she was a US spy because she because--at least her family would be notified. She was threatened by the Iranian officials to confess or she would die without her family where she was.
http://www.cbsnews.com/blogs/2009/05/28/world/worldwatc...
There is an a link to the NPR interview as well with this cbsnews link.
**On the rumored charges of being arrested for buying alcohol:
"I was allowed to call my parents about 11 days , after I told my interrogators, 'Please let me call my father, at least, to let him know that I'm alive.' And they forced me to tell him a lie — to tell him that I didn't know where I was and that I had been arrested for alcohol, but these were not true."
On initially making a false confession:
"I thought, well, if something happens to me, my family doesn't know where I am, maybe they would never find out. And so I made a false confession and I said, 'Yes, I'm a U.S. spy.'"On why she actually liked her eight-year sentence:
"Actually, I thanked God, because I knew that if I had been handed only one to two years, that there wouldn't be such an international outcry. But the eight years seemed so ridiculous."