Dew point is a measure of high humid the air is in an absolute sense--the higher the dew point, the more water vapor in the air.
TQ says "Humidity is independent of the dew point's value"--this statement is absurdly misleading. Let's say you know the temperature alone, is there any way to determine the humidity (either relative or absolute) from that? No, there isn't. However, if you also have the dew point, then you CAN determine the humidity--clearly they are not independent.
In his second paragraph, he says "The smaller (larger) the difference (T - Td) ... the higher (lower) the RH", this is true GIVEN A PARTICULAR TEMPERATURE, but is not true for different temperatures--you can have a larger dew point depression and a greater relative humidity, and a higher dew point will always give a higher absolute humidity, regardless of what the dew point depression is.
Dew point is a measure of how much water vapor there is in the air, so a low dew point means a low absolute humidity. Relative humidity, however, is a measure of how close to saturation it is at a particular temperature, so that can be high despite a low dew point.