Most likely, it is NOT permissible.

Although there are some extremely rare situations that would qualify (such as the employer hires the worker as an Independent Contractor for work that is unrelated to his work as an employee), I would say that 99.99% of the time that is not the case.  

You need to find out why there are payments on the 1099-MISC.  The employee should ask the employer about it, and assuming it is incorrect, the employee should ask the employer to correct it.  If it is incorrect and the employer refuses to correct it, the proper way to file it is to use Form 8919.