Is it possible to have only liquid in a closed container?
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.