Repairing a flat tire

I recently had one tire losing pressure, so I took it to Car-X, where I've previously received prompt and effective service. They found that a nail had penetrated the tire. Years ago I remember tires being fixed by taking a rubber "noodle," heating it I think, and using a needle-nosed pliers to punch it into the hole. The Car-X people told me that what they do is place a patch on the inside of the tire because that's safer.

I wonder if it is safer, or whether I was suckered into a more expensive procedure. It's not a big deal, because it was just $10 for the patch and $30 for the labor, but I'm a little suspicious because they also suggested flushing the coolant because of "high levels of nitrate in the current coolant" and when I declined they quickly lowered the price for that from $130 to $100. I still refused, and I'm always wary when refusing a service results in a lower price being offered. I know nothing about nitrates in coolant as indicators.

Any comments re the best (or safest) way to repair a tire puncture would be appreciated, and any experiences you-all have had with Car-X.