If she got the American Opportunity Credit for 4 years she cannot get it any longer but she may be eligible for Lifetime Learning Credit.
Yes, there is a 4 time limit to claiming the American Opportunity Credit. So, TurboTax will defer to one of the other options. The Lifetime Learning Credit (LLC) is 20% of the tuition paid, up to $10,000 (max $2000 credit). But that credit is non-refundable. It can only be used to reduce her actual calculated tax.
For somebody with low income, it would not be unusual for TurboTax to select the $4000 Tuition and Fees Deduction (TFD) instead of the LLC.
But, there may be a bigger question here: why was the student claiming the American Opportunity Credit (AOC), instead of the parents (or you if she was your dependent). It was worth up to $2500 per year to them. Furthermore, most college age (under 24) students are not technically eligible for the refundable portion (the $1000) of the AOC unless they are an orphan or married, filing a joint return.