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Believe about 10% of what you get off the Internet. I think that they are trying to power a load that has its negative side apriori connected to earth ground without paying attention which way around the line-cord plug is inserted into a USA wall socket, but it wouldn't work anyway.
Why is this a bad circuit. No isolation is only one problem. Getting killed is a problem. I don't like these half wave rectified circuits. Full wave is better.
Look at the top left of the attached circuit:
This has 120VAC input. Neutral and Ground are approximately the same thing. C5 is shorted out by the N to G connected. It works.
Look at the top right:
This has the line and neutral reversed. This happens when the plug is reversed. It does not work! no output!
Look at the bottom left:
Here is 240VAC: based on US power line where 240 is two 120 lines added together.
The current in C2 does not help support the load. It works but C2 is a waste.
Look at the bottom right:
The output is not connected to ground and thus C10 and C11 have a function.
While it is safe to short the output to ground or some thing else, it may not function shorted. There is no real isolation!
I can see why the author thought that two capacitors will cause isolation. I don't think it works like the author thought.
I think Ron is misinterpreting the ground symbol on the output side. This is meant to be a circuit ground and not earth ground. The AC side is strictly hot and neutral with no plug ground involved. At least that should be the intent of the schematic. If not, then all of Ron's observations are correct.
Is the circuit safe in all cases? No. But in an isolated enclosure it would work fine. I have used capacitor connected power supplies many times to avoid cost or weight.