> your employer is also your health insurer

Is this really true? I thought American employers paid the group insurance premium on their employees behalf to the actual insurance companies

Is every org running its own insurance business too?

They are not but the group premiums are deals cut with every business so businesses are incentivized to promote employee health to cut down in their premiums.

Why would they care _after_ they've cut the deal?

Because the deal needs to be renegotiated periodically. The deal may also include incentive structures for continued health initiatives and may include some cost sharing between the company and the insurer.