RETIRED AND RECEIVING A 1099-MISC

I am retired and received a W2 with the employer-paid cost for health insurance for myself and my domestic partner as non-taxable income under box 12a, code DD.  I also received a 1099-MISC  showing the employer paid cost for only my partner's coverage (1/2 of the amount on the W2) under box 6 (Medical & Health Care Payments). Is this correct?  Do I need to file a Schedule C as Self-Employed because of this coverage?  Why wouldn't the taxable portion (my partner's) be included on the W2 as taxable rather than the 1099-MISC? Can this be reported under "Other Income" to avoid getting hit with the Self-Employment tax?