1099-misc for internship stipend

1099-misc form was issued for summer internship that had approx: $3600 of compensation in box 7 (non employee compensation). In an employment statement the non profit org. Clearly stated that I was hired as a temporary , full time employee. The employment memorandum goes on to state that because I was earning class credit for the law internship that I was ineligible for a salary. Instead I would be paid a stipend for living expenses of $3600 in five equal payments.

When I learned that the 1099-misc required me to pay self employment taxes I asked the employer if they had incorrectly issued me a 1099-misc and should have issued me a W2?
The responee I received was "Since you were receiving class credit for your internship we weren't able to put you on our payroll and therefore we cannot issue you a W2".

Are there any IRS rules/laws to support the premise of their response statement?

Since they clearly state I was hired as a full time , temporary employee I believe they should be required to report my stipend as wages on a W2 form and the 1099-misc is only for non employee compensation. Am I right?

Also is it possible that they could report the stipend as an award and therefore put it in box 3(other) of the 1099-misc? This would effectively eliminate the self employment taxes caused by box 7 reporting.