Say someone in your family needs $100,000 to pay for a kidney transplant. How would you raise that? If you have assets you could downgrade, like going from a 4,000 sq ft house to a 2,000 sq ft house but you would be fine otherwise? I consider you rich. If you can stop buying a new car every three years to cover it? You are rich. If you have nothing you could sell or stop doing and will have to go into massive debt, you are probably middle class or lower.
Yeah, it isn't a perfect guide, but the point is actually having things of value is part of what makes you rich. Having things of value based solely on debt you can't manage makes you stupid. Getting interviewed complaining about how poor you are with your $80,000 car makes you a prick.
Result: Employee pays the same, but gets contraception covered; Employer pays just a little bit less; Insurance company chips in the difference needed to cover contraception.
So yes, your employer does pay for some of your health care services if you get insurance through work, since they have to pay essentially half the cost of the policy. But unless your employer is a religious organization, it won't really have any impact on them, unless your health care plan did NOT include contraception. Now, they are just required to choose a health care plan that includes contraception.