No, a diode as part of a rectifier network can fail in a way that it starts letting current through imperfectly causing a high ripple. That's why those handheld testers report on ripple. If you have >100mV your car will still likely function but it's an indication you have a diode starting to go. It's a very tricky thing to diagnose and may cause weird gremlins to happen in the car's electrical.
There absolutely are bad rebuild shops. Unless you are hovering over the guy's shoulder you have absolutely no assurance that all the necessary parts were replaced, and of good quality. A unit can be built with crappy parts and still test well electrically or function for a long time. There's dozens of ways that shortcuts can be taken. Using generic voltage voltage regulators is a prime example. If the guy is only charging $100 for a rebuild do you really think he's sourcing an OE regulator which costs at minimum $50??