So to expand on what the others have said:

1. The corporation does not pay any income taxes.
2. The corporation needs to pay the shareholder "Reasonable Compensation" and give the shareholder/employee a W-2, and the corporation will file/pay payroll taxes (Social Security and Medicare, Unemployment, etc.).
3. The shareholder/employee will enter the K-1 and W-2 on his 1040.  Both are only subject to income tax, not Self Employment tax.
4. If the corporation issued the shareholder/employee a 1099, or the shareholder/employee is otherwise reporting the income on Schedule C of the 1040, that is wrong.  The corporation needs to issue a W-2 (and file/pay all of the associated payroll forms).