Regarding 1099-MISC and amending a Schedule C

So, my wife gets paid 1099 and received a 1099-MISC for tax year 2019.  She does not own the business.  The payer's TIN is different from the recipient's (her) TIN on the 1099-MISC.  She filed her 1040 without adding the Schedule C, which appears to have been a mistake on our part.  The payers  name is obviously different from hers since the payer owns the business and she does not.  However, it appears as though the tax code indicates she must add the Schedule C because it recognizes her as self-employed.  First, is this correct in this specific situation where she does not actually own the business?  Second, her tax software asks for name and address of the business as well as WHO THE BUSINESS BELONGS TO (with a drop down box that only allows her name to be chosen).  Does she choose her name simply because the payer and the tax code recognizes her as the owner of the business?  This is new to us and obviously we want it done correctly.  PLEASE HELP!  Thank you.