There might be a tiny amount of DC in the electronics in the EVSE, but the elephant in the room is 70+kWh of 400V+ DC in the car.
But what sort of plausible fault can cause that DC in the car battery to actually result in a DC current flowing in L or N of the supply to the charger? It's isolated from the chassis (with isolation monitoring), and the charger is also isolated.
Conversely, the DC in the pilot signal in the cable will definitely cause DC to flow if there is a short between pilot and N in the cable, which is a very plausible type of fault, just requiring a worn cable.
Note also that it is tiny amounts of DC we are looking for here - anything that results in large currents is going to cause a big bang and blow fuses etc. It's the relatively tiny leakage that can go unnoticed, saturating the RCD and causing it to not trip when a more serious conventional fault comes along.
Both those videos have rather dodgy use of physics in their descriptions, but correctly point out that pure DC desensitises conventional RCDs.
The sparkyninja one concludes that you should be using Type A rather than Type AC to solve this problem - when in fact Type A also suffer from the problem, and indeed it's manufacturers's data for a Type A device that he uses in his description! The other video makes no suggestion as to what you should do about it, but lumps together railway systems (thousands of DC amps in a circuit with one side earthed), solar PV systems and common household equipment with electronic converters - without discussing what kind of fault might actually result in DC flowing in the L or N of the supply system.
Neither video makes the point about the main difference between Type AC and Type A - that Type A responds to pulsed DC as well as pure DC. Many products rectify the mains voltage to drive a switching power supply or a motor drive, but a short circuit to earth from the 'DC' point after the rectifier on the primary side will result in pulsed DC not pure DC because the rectified DC is not referenced to earth. A short from the secondary side of such a device won't cause any leakage at all since there isn't a current path to either L or N.
To cover all possible faults in the new world of electronic appliances requires Type B, but they are expensive. Most likely faults in these devices with electronic PSU or motor drive will in fact trip a Type A, and Type A costs very little more to make than a type AC. Therefore there is a strong argument for using Type A in most general purpose circuits since they are quite likely to contain electronic loads. Type B would be better, but they are sufficiently expensive that they aren't currently justified except in cases of high risk (as was the case 30 years ago when RCDs of any type were expensive and were only used in cases of high risk, while they are now so cheap as to use them everywhere).
Whether or not EV charging actually has a significantly higher risk of pure DC faults than any other appliance is questionable; the regulation writers evidently think that it does. It is hard to see that the charger itself within the EV has materially different risk compared to other things with similar circuitry like washing machines or air conditioners. The charging cable pilot signal is a clear potential source of DC faults, but a maximum of 12mA; although this is greater than the 6mA that Type-A RCDs are required to tolerate while remaining within spec, you might guess that many devices in practice will actually be OK at 12mA (note that the demonstration in the 2nd video above used 250mA). I haven't seen detailed risk analysis to justify this point.