Speaking as someone who grew up on a grain farm and has owned a farm, this is correct. Obviously it is hard to generalize but low or no tillage farming has vastly lower soil erosion compared to conventional or organic tillage practices. For some reason, people have the set idea that organic practice must be good because its what our forefathers did. In reality, little we do regarding farming is actually sustainable. You are hauling tonnes of material away from the field every year. Those things are not going back, whether you are organic or conventional.

Also, it is a matter of relative severity of problems. Soil loss is much worse than depletion of soil nutrients. As said, organic is potentially much worse for soil loss (although different practices like intensive use of cover crops can help).

no-till is incompatible with organic farming? Hadn't heard about that, a shame if true. I'm not a farmer, but I had heard there were a variety of strategies that would qualify as organic, e.g. cover crops that choke out the weeds, or plastic sheeting over the ground to bake the weeds & pests.