I agree with jkh. The item in the pic is the tension weight, if it spins freely and moves up and down in it's guide freely it is probably good. Judging by the color of the cable, the cable may need replacing. If they couldn't get the gov to set, most probably it's the flyweights on the governor. Most places require trained elevator men to perform the tests, safety reasons, and if you lost faith with the company the easiest thing is to get a second opinion or search for another company
