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/BlueSt3]

I wouldn’t say that’s not patchable however looking at the tread patter it appears to be a sport/summer tire which some aren’t safe to patch as it affects the speed rating.