You are correct that if you have no Earned Income, you would not qualify for an Education Credit.
If your parents provide over 50% of your support (housing, food, medical, etc.) then they can claim you as their Dependent.
Since you are over 25, you will be considered an 'Other Dependent' on their return.
However, since your 1098-T shows a Tuition amount of $13,450 and your Scholarships were only $5,700, they should enter your 1098-T in their return to claim an Education Credit.
The part of your Education Expenses that was paid with loans is considered to be paid by you.
Click this link for more info about How to Enter a 1098-T.
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