What I Don't Get

I just don't understand insurance.

I was looking over my "explanation of benefits" for my hospital stay with Monkey, and if I am looking at this right (which I assume I am, as the form seems pretty self explanatory), my insurance company wants me to pay a deductible for an amount more than I was billed.  The insurance company received a bill for $3.4K from the hospital.  But they have a contract rate of $5.5K but will only pay them $1.7K... so they want me to pay a deducible for the $5.5K-$1.7K which is $3.8K... I don't know about you but wouldn't it be easier for me just to pay $3.4K.  Why do we have insurance again?

And what confuses me further is the hospital called last week, to tell me I owed $45 co-pay (which I paid) for Monkey's birth... they never mentioned wanting $3.8K.

Really, this is terribly confusing.  Wouldn't it save everyone involved money (and time) if the insurance paid against the actual bill and not against this arbitrary "contracted rate".  

I have an e-mail into our HR (hopefully she'll do something this time) and our insurance agent about this, it just doesn't make sense.  I would think HR would be all over it; as my company only requires us to pay $1.5K in deductibles, they pick up the rest.

Insurance reform really needs to start with the insurance companies, and cleaning up messes like this.