How is your situation different from this example in Pub 970?

Example 2. The facts are the same as in Example 1, except that Joan reports the entire scholarship as income on the tax return. Because Joan reported the entire $2,000 scholarship as income, the qualified education expenses don't need to be reduced. Joan is treated as having paid $3,000 in qualified education expenses.

Doesn't this mean that if she chooses not to use the scholarship exclusion, she can claim the AOC?  Isn't $2,500 better than 10% tax on $5,037?