there is the generic medicare levy, which we all pay (well, most) - then there is the medicare levy which is an additional 1.5% (i think) if you're over a certain income bracket and don't have hospital cover

I think the income is $80 000 for a single, so not sure what it is for a couple. In the end you really do have to weigh up how much you will use versus the cost of PHI versus any savings at tax time.
You also need to be aware that most PHI has limits for how much you can claim for each 'area' in a year. So you might only be allowed $1000 (eg) for physio per year and still have to pay full price for anything over that. PHI also doesn't cover all costs - so when I go to the chiro, I pay $20 instead of the $45 full fee.
For the hand surgery, it will be deemed an existing illness, so you will have to wait 12 months to be covered for that (can you wait 12 mths to have it done?) and depending on the PHI you may have a hospital excess and also the surgeon may charge above the scheduled fee and therefore still have a gap for him.
There's a lot to consider.

As for your friend saying you are taxed for the medicare levy in your pay, that's not right, it's added on at the end of the financial year when you do your tax return and is calculated on your taxable income (so after any allowable deductions).