Not true. One factor driving the cost of insurance up is that people go to the doctor when they don't really need to. People react differently when they have to pay for a service themselves. When they have a financial stake in choosing to go to the doctor or not, they are more apt to conserve.
An anology would be, if I could buy coverage that would allow me to have unlimited drycleaning of my clothes, I'd get my winter coat drycleaned once a week, and I'd get all of my suits drycleaned on a regular basis... even if I hadn't worn them since the last cleaning.
Sniff...I think (cough) I have (sniffle) a (sniff) cold (a-a-achooo) coming on. Sniff. Time to see the doctor.