1099-nec for a paid internshipIs that considered self-employment?

It depends. Based on the reporting by the institution where the intern was paid, the document received indicates that self employment tax is required.  If you believe this was reported in this way in error, then you would contact them. 

Form 1099-NEC is used to report earnings from independent work such as an internship.  Below is a summary of internship payments from our awesome Tax Champ @Hal_Al

Was the "internship through his college"? Depending on the details, there are three different ways the income should be reported:

1. If you worked for the school, it could be reported as taxable Scholarship (stipend). 

2. If it's a one time gig, it can be entered as other income, and entered in TurboTax, as described below. 

3. If you worked for an outside (not part of the college) company/employer training in his regular/anticipated line of work, it probably should be reported as self employment and self employment tax paid.  

Please follow the instructions below to report Other Income (will not be subject to self employment tax):

1. Click Federal Taxes -> Wages & Income and scroll down to Less Common Income
2. Go to the last selection, Miscellaneous Income and click Start
3. Go to the last option, Other reportable income and click Start
4. When it asks, "Any other reportable income?" > yes and then type in a description and the amount to report it on your tax return.
5. TurboTax Online and TurboTax CD/Download will use the same procedure

To report it as self employment income search (upper right) 1099nec > Click the Jump to.. Link > begin your entry