What do you mean by this? The article says that NASA makes an avoidance maneuver when the chance of crash is over 1 : 10 000, SpaceX does it when it's over 1 : 100 000.
They seem to mean exactly what you quoted - a lower risk tolerance means they tolerate less risk, meaning they are more cautious. Doing an avoidance maneuver if the risk exceeds 1/100K instead of 1/10K is being more cautious because 1/100K is a lower threshold than 1/10K.