I have fake 150mm Mitutoyo calipers. They worked really well for about three years during which time I never knew they were fake; bought from Amazon first party, not suspiciously cheap, worked smoothly and seemed accurate. As it was my first calipers I should have known that they should turn off automatically and these did not.
It's actually confusing watching that video. By some measures mine appear genuine (case details, paperwork quality, battery supplied, battery compartment, printing), on others it matches the fakes (depth rod mill, no dashes on battery insert, recessed origin button). I think it is possibly just a superior fake compared to what's out there now.
Now I have 300mm "Neiko" calipers. Just as smooth, not pretending to be anything else, turn off automatically. Almost certainly the same as the Shars calipers as mentioned in the video.