And is that in fact the standard set for training in the US (not military)?
That's a non sequitur, it is not relevant to the discussion. And you know the answer already, because you know the FAA does not require full-downs at the private and commercial checkrides. So surface type is
almost moot in the US unless actually practicing full-downs. I say "almost" because there is the possibility of an "accidental full-down". I know this because I have to admit to having an "accidental full-down" once when I was late rolling on. I am happy to report it was on asphalt and that ground slide was less than a skid length
However, learning experience for me: I just looked at the FAA CFI-H checkride PTS and there is absolutely no performance standards other than to properly perform the maneuver! I was surprised! But this does not mean that I support the use of grass or other challenging surfaces to motivate proper airmanship. That should be the province of the instructor.
In thinking about this even more critically, there must be some value in practicing on grass in order to see what it feels like to slide on it. But the question is whether that juice is worth the squeeze in a civilian environment. In a military environment where money is effectively unlimited for replacement of balled up helicopters, there is no cost of insurance, no danger of civil lawsuits, and training helicopters with much greater margins of performance, an assumption of the greater risk probably makes good sense. But in a civilian environment the costs to the training environment compared to the costs incurred by actual EOL emergencies don't justify the return on investment. And this is why the FAA training requirements appear to be so weak, but are actually saving lives and equipment overall. I.e. the total number of fatalities and accidents per year associated with EOLs was higher because there were too many happening in training. With the "relaxed" standards people seem to be crashing and dying at the same rate after training, and a lot fewer during training, so a net improvement.
P.S. I edited this because my original last few sentences were not clear enough.