What I meant with "you have to wait months" is that if you go with the government-provided doctors and processes, they put you on a list and you have to wait for your turn. Getting an exam done can take months, and you can wait years for surgery, unless your condition is life-threatening.
If you go to a private clinic, of course you can get test results the same day and schedule any surgery within days.
Most people who can afford it go the private route. I had to do that too, which kind of pissed me off since I pay a hefty amount each month for insurance and I still have to go to private clinics. BUT, using the public infrastructure is just too inefficient. To get blood exams at a reduced price I had to schedule an appointment with my GP (days in advance), she'd send me to a specialist (about 1 week wait to get appointment), then a specialist would give me the paperwork required to get SOME of blood tests I needed covered by my insurance.