The law is written the way it is. If she is not attending "full time" as the college determines, and she earned more than $4300, she can't be claimed as a dependent.
You don't really file as "independent", you either answer yes or no to a question that asks "Can you be claimed as a dependent by another taxpayer" and this year at least, she answers "no."
For 2020 only, this will make her eligible for $1800 in COVID stimulus tax rebate.
In general, this means that she will report her 1098-T on her tax return instead of her parent's return. It will likely mean a smaller AOTC credit, unless her earnings were well over the standard deduction of $12,400, since that credit is not refundable for students under the age of 24. (It can cancel the tax she owes, so she should get a full refund of any withholding, but the excess can't be added to her refund.)
If she receives a scholarship that is less than tuition (and reduces the tuition that someone has to pay) that is not taxable and does not change with changing her status. If she received a scholarship that was more than tuition (covers room and board, for example) then that is always taxable income to the student, and does not change with the change in dependent status.
