Wow, strange story!
As far as what the bike shop said -new tubes?
Seriously, I've never had to replace tubes in a bike ever that weren't totally tore up that I couldn't get a patch on them. Tubes on 30-40 year old bikes are like new usually inside the tire, and are often of better quality than many tubes that come new today.
I've had a few Schrader tubes that needed to have the stems reamed and re-tapped so they seal with a new stem put in -but a tube is pretty protected inside the tire from not only harmful ozone gas that eats rubber, but UV rays from the light that also degrade them.
Whenever I hear someone say that a bike needs "new tubes" I usually roll my eyes. Replacing tubes and NOT replacing the tires? Gaffaw!