Who reports a dependent's employer-provided tuition assistance reimbursement?

If your student is claimed as your Dependent, you claim her education expenses on your return, no matter who paid them, so enter the entire tuition amount paid. 

In the 1098-T section, you'll be asked about employer benefits received. 

Depending on the amount of assistance her employer gave her, the first $5250 is non-taxable.  The balance of that (if there was one) would be included in Box 1 Wages on her W-2. If she was taxed on a balance over $5250, enter only $5250 as employer received benefits, since tax was already paid on the balance.  

The amount qualifying for an Education Credit, would be the tuition amount, less scholarships/grants in Box 5 of the 1098-T, less employer assistance, 

Here's more info on Employer Education Assistance and Education Credits.

@CSWolf