I don't get it - please elaborate on what you did exactly in this test. Mains power and finger in the same sentence sounds dangerous.- SonOff powered with main AC Power AND wire between 2 finger to 3.3vor gnd pin : With OK !!!
ESP8266's are a "spikey" load.
The sonoffs have very little capacitance on the 3.3V side - according to the schematic 22uF at the regulator output and some small ones around the chip. Ceramic caps are usually rated for 20% tolerance so in worst case the esp has to rely on less than 18uF. On the supply side is a bigger electolytic cap, maybe they cheaped out on that and it could be wise to support the regulators input with a 10uF ceramic (low esr) like the AMS1117 datasheet suggests.
Retrieve yours from the bin and add a big cap (470uF) as close as possible to the chip, that should help with stability.
I share your experience with a sonoff running wonky from its own AC supply but stable through a cheap AMS1117 module (which has 10uF + 100nF ceramics on both sides - input and output). Without an oscilloscope it's guesswork but I feel the regulator itself isn't running stable in the original circuit design. I have parts coming and will try to improve it.
The customer support's answer is miserably anyhow...