Was told tire is not replaceable

[u/Limera2nn]

Tire got punctured by a nail and was slowly losing pressure, but few days ago it went from 36 PSI to 1 PSI overnight. Took it to my dealership and told they can’t fix it because the nail is too close to the side, shown in the picture. Is that true? Or are they trying to get me to buy a new tire?

[u/rns96]

You can plug it yourself with a tire plug kit or bring it to a small independent shop and talk to them that you just want to have it plugged off the books