Health insurance isn't a business with such fat margins as to account for a difference between a $1500 MRI and a $98 MRI, say. That's the kind of rate the doctor charges the insurer, which in turn passes it on in a derivative way. The insurer is the customer.
Now, why doesn't an MRI cost something batshit insane like $1500 in other countries where the practitioners are also private? That's an interesting question. I don't think the cost controlling abilities of government committees or agencies account for the whole story; historically, committees of any kind - in the public or private sector - are pretty bad at keeping a lid on costs.
Still, I'd point the finger much more at doctors' profits than insurers' profits, though obviously neither is irrelevant.
I think this rather famous article treats of the matter fairly well:
http://www.newyorker.com/reporting/2009/06/01/090601fa_fact_...