The math is fine right up the 2nd to last paragraph where an assumption is made that is incorrect. It matters a lot what the output section topology is. An excellent example is the difference between a triode gain stage and a cathode follower using the same triode. The CF will be found to have a lower output impedance, according to Rp/1+mu where Rp is the plate resistance and mu is the 'voltage gain' of the tube.
So if we take the example given we get 17.5/3 = 5.767 (the mu of a 6AS7G is 2), which is for a simple CF circuit. For a Circlotron, which is a CF variant, the formula is similar, the 1 is replaced by a 2 as above so we get 17.5/4 = 4.375
In these cases it is assumed there is no feedback.