IMO, the point is moot.
It is as simple as....DONT HIT THE DIRT. In MANY years of cutting firewood, downed trees, tops, etc to the tune of 25-30 cord per year, I have NEVER been in a situation where I HAD to go into dirt. There are ways/techniques around that. Hence: why the OP is asking questions. And simple answer is...NO its NOT ok to cut into dirt.
Well, I guess I shouldnt say never, because cutting stumps/roots below ground level is a different story. And even when clearing ALL the dirt possible, you have to change chains VERY frequently.
Fortunatally, we dont cut stumps very often.