Knife Skills Illustrated: A User's Manual suggests that knives can be cleaned with hot running water alone. "With sufficiently hot water, soap should not be necessary." Is this safe? What if I am only cutting vegetables? What if I am also cutting raw meat?
In order to "Sanitize" any surface you must wash that surface (in this case, knife blades) with water at no less than 190°F (~88°C) according to the (U.S.A) National Sanitation Foundation (NSF). Earlier this year the Conference for Food Protection recommended reducing that standard to 160°F (~71°C) as an "energy saving measure" citing a study at Ohio University that claims that it is equally effective. Additionally they recommended that the temperature could be reduced to 120°F (~49°C) with 'chemical additives' (soap).
So the question is "How hot is your hot running water?" According to "Wikipedia" (a dubious source at times, but I will accept it for this point) suggests that most home water heaters produce water at 104°F (~40°C) to 120°F (~49°C). This would suggest that to sanitize a knife blade something more than 'hot running water' is necessary. In fact since water over 131°F (~55°C) puts you at risk for scalding (Wikipedia, Ibid) and you certainly don't want a water heater putting out water that hot, I would have to disagree with your source and conclude that in household use soap is required to sanitize your knife blade.
note: in order to qualify my answer to the question of "safe", I have elevated the standard from "clean" to "sanitized", certainly you may 'clean' a knife with running water but that level of clean is not what I would consider 'safe'.