A good enough test is to stop somewhere flat, put the car in fourth, and see if you can get it to go. Mind, that only applies if it's a manual, if it's an automatic this won't work...
But do take it to another shop and see what they say. I learned to drive stick in my Honda, which now has 130 000 km on it, in a hilly neighbourhood, and use the clutch to downshift, and it's been fine...
On another note, someone kindly explain "rev matching". It's not a term I've heard before...