If the $13k was added to the employee's W2 (i.e. if box 1 contained another $12912 and box 12 (code DD) had $23112 (1926 x 12) instead of the current $10200 (850 x 12)), the net result in taxes for both employee and employer would be the same.

If the $13k appeared on a paycheck as a salary increase, and the employee used it to buy (or not) insurance of their choice, the employer and employee would each end up paying about $988 SS and Medicare taxes on it:
1076 x 12 x .0765 == 988

Self-employed people already know about that latter point: yes, we get to write off (1040, line 29) the entire cost of our SE health care premiums so we don't pay state or federal income tax on it, but that's after we calculate SE tax on total net income (Sched C, line 31).