How does a distribution from a 529 plan to pay for tuition affect getting a tuition deduction?

You are correct in that the same expenses cannot count in both areas, but it is useful to use 529 plan funds with their tax favorable status. These funds are not taxed if all distributions went toward qualifying education expenses,  including K-12 tuition, or room and board. The amount distributed will be reported to you on Form 1099-Q. Report this first, before entering Form 1098-T.

Form 1098-T is the form used to report tuition and scholarships as received for qualifying education expenses. Form more information, see: Where do I enter Form 1098-T?

If you already started with Form 1098-T before entering Form 1099-Q, go back to both of these areas of the return and delete each before re-entering them.

TurboTax will optimize the best benefit for your circumstances. For  more information, see: The Lowdown on Education Tax Breaks

It takes $4000 of tuition to claim the maximum $2500 AOTC tuition tax credit. That's a direct reduction in calculated tax, not just a deduction in income before tax is calculated. 

So, yes, it is best not to pay all expenses with a 529 plan distribution.  

But, as others have said, room and board, as well as books and computers are qualified expenses for a 529 distribution.  

Even if you already took too much 529 distribution, it is better to pay a little tax, on the distribution, than to forego the tuition credit, See example below.

______________________________________________________________________________________

Qualified Tuition Plans  (QTP 529 Plans) Distributions

General Discussion

It’s complicated.

For 529 plans, there is an “owner” (usually the parent), and a “beneficiary” (usually the student dependent). The "recipient" of the distribution can be either the owner or the beneficiary depending on who the money was sent to. When the money goes directly from the Qualified Tuition Plan (QTP) to the school, the student is the "recipient". The distribution will be reported on IRS form 1099-Q. 
The 1099-Q gets reported on the recipient's return.** The recipient's name & SS# will be on the 1099-Q.
Even though the 1099-Q is going on the student's return, the 1098-T should go on the parent's return, so you can claim the education credit. You can do this because he is your dependent.

You can and should claim the tuition credit before claiming the 529 plan earnings exclusion. The educational expenses he claims for the 1099-Q should be reduced by the amount of educational expenses you claim for the credit.
But be aware, you can not double dip. You cannot count the same tuition money, for the tuition credit,  that gets him an exclusion from the taxability of the earnings (interest) on the 529 plan. Since the credit is more generous; use as much of the tuition as is needed for the credit and the rest for the interest exclusion. Another special rule allows you to claim the tuition credit even though it was "his" money that paid the tuition.
In addition, there is another rule that says the 10% penalty is waived if he was unable to cover the 529 plan withdrawal with educational expenses either because he got scholarships or the expenses were used (by him or the parents) to claim the credits. He'll have to pay tax on the earnings, at his lower tax rate (subject to the “kiddie tax”), but not the penalty.

Total qualified expenses (including room & board) less amounts paid by scholarship less amounts used to claim the Tuition credit equals the amount you can use to claim the earnings exclusion on the 1099-Q. 
Example:
  $10,000 in educational expenses(including room & board)

   -$3000 paid by tax free scholarship***

   -$4000 used to claim the American Opportunity credit (AOTC)

 =$3000 Can be used against the 1099-Q (usually on the student’s return)

Box 1 of the 1099-Q is $5000

Box 2 is $600

3000/5000=60% of the earnings are tax free

60%x600= $360

You have $240 of taxable income (600-360)

**Alternatively; you can just not report the 1099-Q, at all, if your student-beneficiary has sufficient educational expenses, including room & board (even if he lives at home) to cover the distribution. You would still have to do the math to see if there were enough expenses left over for you to claim the tuition credit. Again, you cannot double dip!  When the box 1 amount on form 1099-Q is fully covered by expenses, TurboTax will enter nothing about the 1099-Q on the actual tax forms. But, it will prepare a 1099-Q worksheet for your records, in case of an IRS inquiry.

On form 1099-Q, instructions to the recipient reads: "Nontaxable distributions from CESAs and QTPs are not required to be reported on your income tax return. You must determine the taxability of any distribution." 

***Another alternative is have the student report some of his scholarship as taxable income, to free up some expenses for the 1099-Q and/or tuition credit.