The problem with “if done properly” is that you actually have to go and check. If you just “hope that it is done properly” you can have a lot of surprises, like lights going out when the sink gets full of water. Or spicy dishwashers.

If you don’t know whether it’s properly done, it’s much more efficient to throw a ground cable from the nearest service junction than it is to “hope” and then have to fix things later.

It’s not about whether or not pipe is a good ground. The electrical grounding for a building needs to be like a tree. No ground loops and exactly one grounding point. Arbitrarily adding grounds, especially through water pipes can do things like making all of the piping and water in the house hot if there is a fault somewhere and it definitely seems like that’s the case here.

The whole idea is that the ground wire is the least resistance path for stray current to go to. When you have separate ground paths there can be a dangerous potential between ground wires and the least resistance path for stray current can again be you.

There's a difference between the electrical return path (aka neutral) and protective earth (aka ground). Earth is purely for safety: you earth the metal chassis of appliances so that if for some reason they get shorted to hot, the current has a low impedance path to earth and your breaker will pop. It's perfectly acceptable to have an independent earth at every single outlet, as long as you're earthing to an acceptable source (which, AFAIK, means driving an earthing rod into the ground, because pipes aren't legal in the NEC anymore).

The "single ground point" is some sort of weird misconception of how ground systems work that became an urban legend. I think it comes from the fact subpanels used to be allowed to bound the neutral and ground and that putting a ground rod there created another return path for current from the neutral.