Turbotax says room & board are qualified ed expenses if paid for from a 529 plan distro. IRS.gov says room & board OK only if paid with Coverdell ESA, which is correct?

The IRS states on pages 50 and 51 of Publication 970 Tax Benefits for Education for Qualified Tuition Program  (529):

Expenses for room and board must be incurred by students who are enrolled at least half-time (defined later). The expense for room and board qualifies only to the extent that it isn't more than the greater of the following two amounts.
a. The allowance for room and board, as determined by the school, that was included in the cost of attendance (for federal financial aid purposes) for a particular academic period and living arrangement of the student. 
b. The actual amount charged if the student is residing in housing owned or operated by the school. You may need to contact the eligible educational institution for qualified room and board costs.

Click here to see further information in Publication 970.

You're reading it wrong.  Room & board are qualified ed expenses for a distribution from a Qualified Tuition Plan (QTP). Both ESAs and 529s are QTPs. 

Note: you don't have to have literally paid for room and board with the QTP money. You only have to have had qualified expenses in the same year that you took the distribution.