Rear Tire \ Tyre Flat With Small Nail - Replace Tire Or Tube Only?

Rear tire on T100 picked up small thin nail in center of tread and went flat overnight. Holds air maybe 20 mins. Tire has 3700 miles on it and tread is ok. See pic. Will bring in to dealer but what are some member opinions if I should just have tube replaced or also the tire?

 

Thanks guys. Makes sense to me and gives me conviction. Had stopped for by dealer without bike described situation one mechanic was trying to scare me into new tire on basis of safety. To be fair they hadn’t seen it or pic. Better use of money will be to buy the center stand from them...