Is it possible to have only liquid in a closed container? I recently read an answer by Aman Rusia for this question: Is a liquid in a container always in equilibrium with its vapour?

In it, they say that 


  You can't have a container filled with only liquid. Think about that
  for a moment. Similarly you can't have a container filled with only
  ice. Some water, or water vapour, or even combination of the two will
  appear alongside.


However, my textbook says that 


  Imagine that you have a sample of water in a cylinder fitted with a piston at low pressure. Suppose that the temperature is held constant at 50 °C, and that weights are placed on a piston to exert a pressure of 1.0 atm. Only liquid water is present. The piston presses on the surface of the liquid. Now gradually reduce the pressure by removing some of the weights. At first, nothing seems to happen. The high pressure is keeping all the water molecules in the liquid state, and the volume of a liquid changes very little with pressure. However, when so many weights have been removed that the pressure has fallen to 0.12 atm (the vapor pressure of water at 50 °C), vapor begins to appear. The sample is now at the vapor-liquid boundary on the phase diagram. The pressure remains constant so long as the liquid and vapor phases are both present at equilibrium and the temperature remains constant. You are free to pull up the piston by an arbitrary extent, but enough water will evaporate to maintain the pressure at 0.12 atm. When you pull the piston out far enough, the liquid phase disappears; you are now free to modify the pressure of the vapor at will.


Atkins, Jones, and Laverman, Chemical Principles

So, is it true that you can have a container filled with only liquid?
In a tight, solid vessel, you can of course have a liquid (or any condensed phase) completely fill it. 

There are basically three possibilities


the inside is at (potentially very) high pressure. no problem, water is compressible, just not very much, and also the vessel has a finite $E$ modulus
the inside is just at the vapour pressure of its content, but (because of the different expansion coefficients of vessel and content) the temperature must be kept perfectly constant at exactly the level where this is the case
the inside is below vapour pressure, but no gas bubble has evolved yet, that's principally an unstable condition, but if the deviation isn't large, it can stay practically forever.


Because of surface tension, there is even a small pressure range where the last case is actually stable.

I say your statement is basically right: You can have a completely filled vessel, but you can't do anything useful in it before it either bursts or bubbles.