Dew point variation in a day
From a review of weather observations, that statement is false.

Below are  the synoptic weather maps for Australia for 11 August 2015 and  12 August 2015. There are no weather fronts, or adverse weather in the western two-thirds of the continent.





Alice Springs (lat:-23.8, long: 133.89) is in the centre of the continent. It's weather observations for 11 August 2015 reveal the temperature ranged between $5.8$ $^oC$ and $26.0$ $^oC$ and the dew point  range was between $-18.8$ $^oC$ and $-2.5$ $^oC$.

Similarly for Darwin (lat: -12.42, long: 130.89), which is located on the coast in the sub tropics, in the central north of the country, the temperature range for 11 August 2015 was $19.7$ $^oC$ to $30.1$ $^oC$, while the dew point range was $15.4$ $^oC$ to $19.8$ $^oC$.

Perth (lat: -31.93, long: 115.98), on the southern western coast has a temperate Mediterranean climate. It's temperature range was $10.2$ $^oC$ to $17.6$ $^oC$ and the dew point range was $5.7$ $^oC$ to $11.7$ $^oC$.

Adelaide (lat: -34.95, long: 138.52), on the southern coast, in the centre region , also has a temperate climate and its temperature ranged from $7.6$ $^oC$ to $15.4$ $^oC$ and the dew point range was $-0.3$ $^oC$ to $8.5$ $^oC$.

Lastly, Brisbane (lat: -27.39, long: 153.13) which is on the east coast  had temperatures between $8.2$ $^oC$ and $21.9$ $^oC$ and the dew point varied between $6.9$ $^oC$ and $15.8$ $^oC$.

All these weather observations show significant variance in the dew point for these locations given the respective temperature ranges and the lack of weather fronts and adverse weather systems.