Understanding PSD: Why Does Power at High Frequencies Affect Low Frequencies?
The spectrum allows you giving another complementary look on the data.
It is the other side of the same coin.

In Frequency Domain we are looking on the energy of each spectral component of our data.
Each component is independent of other component in the meaning each component is orthogonal to any other component.

In the case of White Noise, the PSD is the Fourier transform of the Auto Correlation function.
The model is Continuous White Noise is one which has infinite power.
Its power becomes finite once it is sampled by a sampling chain which has Low Pass Filter (Which the component which limits the incoming power) and AD.  

Now, just like LPF will limit the power of any signal which has bandwidth which is higher the LPF bandwidth it does so to White Noise as well.

Namely, the Constant Level of the PSD is a property of the White Noise alone (In case of Gaussian White Noise it is the $ \sigma $ parameter) while the power of the sampled noise is derived by the level of the PSD and its bandwidth (Which is a property of the LPF).

There is no high frequencies which changes the values of low frequencies.
The power gets bigger because of the hidden assumption that when you sample with higher rate you use LPF with higher bandwidth which lets more frequencies in and hence more power.