It sounds like the program is using 10,000 of the expenses towards the Lifetime Learning Credit rather than for the distribution. Using 10,000 expenses results in a 2,000 credit.
That 2,000 credit lowers your tax liability, by 2,000. (1040 line 20)
Claiming 10,000 distribution is not claiming 10,000 taxable income, the taxable portion is computed based on the ratio of earnings and basis (your contribution). You are only taxed on the earnings portion. (9268/12699 x 10,000 = 7,298) I'm two dollars off, but perhaps there is rounding involved.
It depends on your tax bracket, but the tax on 7,298 should be less than the 2,000 tax credit.
(FYI, if you were attending at least half-time at least one period, you can allocate the distribution to room and board as well as tuition fees books and supplies. The housing need not be on campus but can't be more than what the school would charge. Room and board expense also offsets a 1099-Q)
If you don't want to claim an education credit, you can type letme into the searchbox
Click the "jump to letme " link
(the searchbox is a bit funny this season and you may need to click after typing in the searchbox to get back into the program search)
Here you can change the credit or allocate a different amount to apply for the credit.
IRS Pub 970 explains further
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