Education

Yes, you are correct. 

The housing allowance is not reported AND that amount has nothing to do with earning an education credit. It DOES NOT reduce the tuition paid. 

Chapter 35 DEA is administered through the VA and treated the same as a basic housing allowance. 

According to the U.S. Department of Veterans Affairs:

Any veterans’ benefits paid under any law administered by the Department of Veterans Affairs (VA) should not be reported as income to the Internal Revenue Service (IRS). You will not receive a W-2 from the VA.

Per IRS Publication 970:

"Payments you receive for education, training, or subsistence under any law administered by the Department of Veterans Affairs (VA) are tax free. Do not include these payments as income on your federal tax return.

If you qualify for one or more of the education benefits discussed in chapters 2 through 13*, you may have to reduce the amount of education expenses qualifying for a specific benefit by part or all of your VA payments. This applies only to the part of your VA payments that is required to be used for education expenses.

Example.

You have returned to college and are receiving two education benefits under the latest GI Bill:

1. a $1,534 monthly basic housing allowance (BAH) that is directly deposited to your checking account, and $3,840 paid directly to your college for tuition.

Neither of these benefits is taxable and you do not report them on your tax return. You also want to claim an American opportunity credit on your return. You paid $5,000 in qualified education expenses (explained in detail in (explained in detail here in IRS publication 970, chapter 2). To figure the amount of credit, you must first subtract the $3,840 from your qualified education expenses because this payment under the GI Bill was required to be used for education expenses. You do not subtract any amount of the BAH because it was paid to you and its use was not restricted."

VA Source