Your understanding is correct in the very broad sense but the devil is in the details. It doesn't necessarily have to be as broad as all salaried, or all hourly paid. I work for a university - we have, literally, 26 employee "classes", each designated by a letter of the alphabet. Each and every one of those classes has some variation either in how they are paid or in what benefits they are eligible for. Our plan document very specifically names who is eligible for what. If your employers have a plan document that states that "relatives of the owner" are eligible for health insurance but other salaried employees are not, they are in the clear. Please note that the plan document I am not talking about the employee handbook but the document that outlines any pre-tax benefits.
They are also free to have this benefit as a bonus for certain employees, or to provide it to only family members.
So there are no options here for you to address; no banner for you to take up and fly. There are a number of ways this could be legal; no reason to assume it is not being done legally; and quite frankly, what someone else is getting is none of your business.
I am now going to say that no matter where the check was left, you had no business looking at someone else's check. Yes, you could be fired for that.

