Fluid Pressure: The Collision Model - Approximation or Truth?
The quoted paragraph from the textbook talks about fluids which usually includes gases, liquids, and plasmas. However, it would not be right to say that for liquids (e.g., consider water for concreteness) the pressure is the kinetic pressure $P_k=nkT$. First of all, we know that we can put water under a piston and increase the pressure isothermically at nearly constant density. If the pressure is due to particle collisions then why does it increase without any increase of temperature and density? Furthermore, using the numbers for water at normal conditions, $n=33e27 m^{-3}$, T=300 K, we'd get the kinetic pressure $P_k$ at about 10 million atmospheres, but we don’t see it!
We don't see this huge pressure because it is largely compensated by intermolecular attraction forces. So the total pressure in a liquid is $P = P_k + P_f$, where $P_f$ (negative at normal conditions) is the component of the pressure due to intermolecular forces, strongly dependent on the density. If water is compressed (at a constant temperature) the resulting pressure increase is due to the change of $P_f$.
So, for water compressed under a piston at a constant temperature, the total observed pressure increases; the thermal pressure caused by water molecules bouncing off the surface does not change in this process but the intermolecular forces respond to the compression changing the total pressure.
Given that the thermal pressure in a liquid is almost entirely compensated by the intermolecular forces, one can model a liquid as a large number of slippery almost incompressible balls lumped together, essentially excluding thermal motion from the picture. This model would have the properties of a real fluid (weakly compressible, isotropic pressure, Pascal law, Archimedes law). If we put such a "liquid" in a vertical column then we'd observe that those balls deeper down from the surface are compressed more (because there is a larger weight above them), and a body embedded in this “liquid” deeper would experience a larger external pressure.
The model is a very good approximation as long as the mass of the molecules colliding with the surface have negligible individual mass and cross section with respect to the surface they are hitting. The number density of molecules also matters in some cases because more molecules means more internL forces, which might have an impact on their collision rates and momentum change.
Fluid pressure increases with depth because there are more particles above than below. Consider any surface in the fluid parallel to the base. There is a certain distribution of particles above and below it. As you move the surface down, the number of particles above it increase whereas there is a decrease in the number below it. This causes more net pressure ro be exerted downwards and hence the variation with depth.
As you have already mentioned in the first part, and as I have answered, it is an approximation. The Real Gas equation is a better model (for gases) and there are several others. But for most situations involving low density, low pressure and moderate temperatures, such approximations are quite valid.
Cheers!