I agree that it sounds like this one is unpatchable. A good rule of thumb is that if the nail went through the bottom of the tire, you can patch it, but if it went into the side, you can't.
That being said, I would never, ever pay someone to patch a tire. It is just way too easy to do yourself. The kits only cost five dollars or so and come with about three patches. Additional patches are probably about three for a dollar. The kits come with good instructions, but basically all you do is take the one tool and ream the hole just a bit so the gooey patch will stick. You then put a patch on the other tool and jam it into the hole you made. Pull out the tool and the patch will remain. Clip off the exposed tails of the patch and you are ready to pump up the tire.
Several years ago, I got a nail in my Jeep's tire and didn't realize it. The vehicle sat out overnight and presented the flat as a gift to me the next morning. It took me only a few minutes to find the nail, yank it out, and patch the hole. Unfortunately, I was between air compressers so I used my CO2-based bicycle tire inflater to get enough air in to allow me to drive the Jeep a mile or so to the gas station and air it up. I still made it to work on-time. I could have simply changed the tire and worried about fixing it some other time, but that might have actually taken longer and would have surely been dirtier.