As far as I know the VHI is an additional health insurance in Ireland which deals with addionals like eye surgery, dental treatments etc. The basics health insurance (bhi) are payed with your income taxes.
In Switzerland it is a bit different because you dont pay the bhi in your tax, that is why you have to have the bhi mandatory. But you can choose between different companies and prices.
For all additions you can choose different policies for example Eye surgery or dental t. which cost ~10sfr/month/person.
I would suggest to arrange a meeting with your GP and discuss the issue with him about a non planed visit in a Swiss hospital with beeing resident and dont pay swiss health insurance.
It would be the same as I would tell the state that they have to reduce my tax payment because I pay health insurance in Switzerland.
It dont work like that.