Role of the output capacitor in buck converter in terms of frequency
The recommendation given in the application note is not new and the phenomenon well known. A capacitor is made of several parasitics among which you find the equivalent series resistance (ESR):

This ESR can be revealed by an impedance graph or be extracted from the capacitor data-sheet. For an electrolytic capacitor, the ESR varies significantly with age, temperature, frequency while the capacitance is sometimes affected by the bias depending on the adopted technology. At low temperature the ESR is large while it diminishes at a higher temperature.
When you run a small-signal analysis of the buck converter operated in current-mode control, you end-up with the equivalent circuit:

You can see the output capacitor decoupling the load \$R\$ and it appears with its parasitic term, \$r_C\$. This combination creates a zero in the transfer function. If you go through the equations and determine the control-to-output transfer function of this converter, you should find:
\$H(s)=H_0\frac{1+\frac{s}{\omega_z}}{D(s)}\$
In this expression, the numerator hosts the zero defined as \$\omega_z=\frac{1}{r_CC}\$. This zero is going to change the phase response of the power stage you want to stabilize. Since \$r_C\$ is going to change with temperature and age, it is your duty as a design engineer to make sure the compensation strategy is adequately calibrated to ensure proper operation despite these variations. Monte Carlo, multiple ac simulations or worst-case analyses can tell you how robust your system is in the end.
This zero contribution is also present in linear regulators and you have to carefully select the capacitor to keep away from the so-called tunnel of death where stability can be at stake with certain ESR values. Fortunately, in your circuit, the controller lets you tailor the compensation strategy to account for the ESR variations and other contributors.