What does it mean when its said that most Turing Machines are not programmable?
I think the point being made is that, as you say, the transition rules of any Turing machine are fixed in advance, so every Turing machine computes a fixed function of its input. Since the machine computes a fixed function of its input ("Count the number of 1s", "Determine if the graph represented has a perfect matching", etc.), it can't really be called programmable.

However, for some Turing machines (e.g., universal Turing machines), we treat one part of the input as being a program that should be executed using the rest of the input as input. These machines would be described as programmable in the context of the article you link.



I hereby declare actors to be programmable human beings.