Like others have said, if the rim's braking surface feels concave with little ridges, change it. They dont last forever. Before discs came into my life, I was getting maybe two years out of a rim. Your shop is probably giving you good advice. I have had two rims fail. One when I was topping up the air with a gas station hose-not an issue of over pressure either, I would only tap little blasts of air into the tube at a time and check with a guage. No this rim gave away cuz I was using it past its "best before" date. There I was kneeling down at the wheel, filling it, when ka-boom. I was deaf in one ear for ten minutes.
You certainly dont want a rim to fail like this while going down hill on a curve...