You're getting wishy washy answers because the tax code is complicated and convoluted. The correct answer depends on the details.
Reading between the lines, it appears she sat the kids in your home and not hers. That makes her a household employee and not a self employed person. Because she is your parent, she is exempt from the "nanny tax". That is you don't have to pay her social security and medicare (FICA) tax and neither does she.
So the answer is: she is not required to file because she does not have enough income and also does not have to file just to pay FICA tax.
BUT because you have FSA and/or are claiming the dependent care credit, you have to provide her SSN to the IRS. There is a small chance that she will get a letter, from the IRS, that she will have to respond to. Hopefully, she can explain it away, with the facts.
Some experts might advise her to go ahead and file to avert an encounter with the IRS. The $1500 goes on line 7 of form 1040 (or 1040-A) with the notation "HSH".
