Is it correct that my University issued a 1099-NEC to me for the $1K they contributed to my out of state rent when I did a 30 day rotation for my pharmacy program?

It depends. If the school considers the $3,000 as income due to the 30-day rotation and not rent, they can issue the 1099-NEC. You do not have to own a business to be considered self-employed by the IRS. The IRS examines whether an employee/employer relationship exists and whether social security and medicare taxes were paid on the income received. When the social security and medicare taxes are not paid, and there is no employee/employer relation, the income is considered self-employment income. The income is computed on Schedule C, which is why self-employment tax is calculated.  

Per the IRS, "Self-employed individuals generally must pay self-employment (SE) tax as well as income tax. SE tax is a Social Security and Medicare tax primarily for individuals who work for themselves. "

For more information, see the link below:

• Self-employed individuals