10% penalty for excess 529 plan distributions

I would like confirmation on a point which I state informally below, by paraphrasing the more formal text of Pub.970. It has to do with a penalty of 10% of the taxable withdrawn earnings (in addition to the tax on it) that is in excess of any adjusted qualified educational expense (for 529 plans).

 

My informal understanding of Pub. 970 text on this issue is as follows: One can always withdraw money from a 529 plan up to the amount of a tax-free scholarship without the additional 10% penalty.

 

I want to know if I have correctly understood the formal language of Pub. 970.

 

A specific situation I face is as follows:

EXPENSES
Tuition: 57879
Books: 554
Room and Board: 15990
Total Qual. Expenses: 74423
Scholarship: 9848
Used for AOTC: 4000
ADJUSTED Qual. Expenses: 60575  (=74423-9848-4000)

 

529 WITHDRAWALS
Withdrawal (from 1099-Q Box 1): 70393
Earnings (from 1099-Q Box 2): 10538

 

Based on the above data, I have a taxable amount of 1470 on the earnings owing to a larger distribution than the qualified expenses. (Calculated as [1-60575/70393] x 10538 = 1470.)

 

The question is if I owe an additional 10% tax.

 

Based on my understanding of the rules, as stated above informally above, I think not.

 

Please could someone clarify if my understanding is correct.

 

Thanks very much in advance.