A part time position does sound like Self Employment income. If she got a 1099Misc with the amount in box 7 that IS self employment. If she was an employee she would have gotten a W2 with taxes taken out.
Sorry she had to file schedule C for self employment income and pay the self employment tax. The SE tax is to pay the mandatory Social Security & Medicare taxes the employer did not take out. What kind of work was it? There might be an exception for babysitting income.
