Prompted by ericscott’s comment, I had to tear down the Anonymous White USB Charger to see what caused the bizarre current waveform when connected to the Arduino in a Glass Tile:

Start by grabbing opposite corners in a small vise and gently cracking the solvent-bonded joint between the sections:

Pull the base past the molded latches:

Behold: components!

On both sides of both PCBs!

The top half of both boards, above the isolation cut, handles the line voltage and the lower half handles the 5 V USB output. You’ll note the absence of extra-cost parts like voltage feedback or ahem safety fuses.
The IC on the right half is labeled DP3773, which doesn’t seem to exist, but is surely similar to the LP3773 Low-Power Off-Line / PSR Controller.
Treating the whole regulator as a black box simplifies the schematic:

The cap bridging the two sides should be a Y capacitor, but it’s an ordinary 1 nF ceramic cap with a generous 1 kV rating. As far as I can tell, having it inject AC line noise directly into the +5 V side of the USB supply is just a bonus.
The base markings again:

Whaddaya want for a buck, right?
Yup, there is a Chinese quality fully rated safety fuse. It’s the PCB track at top left. Of course, the ‘smell alert’ users get from the coincident burnt PCB is an added bonus feature.
What I’d like to know is if the transformer includes quality primary to secondary isolation i.e. tape between the turns. That costs an extra 0.2 cents in the factory, so it’s only the best chargers that get that, ah, feature.
Well played!
It’s worth noting the case lacks a fake
CE
mark, so it’s not pretending to be anything in particular.More on fake
CE
marks: https://support.ce-check.eu/hc/en-us/articles/360008642600-How-To-Distinguish-A-Real-CE-Mark-From-A-Fake-Chinese-Export-Mark