Depends, ..
Mr. Babbage tells me we can make a computer out of wood. And our wooden computer can simulate what an electric cable does. And that's what Turing tells me. Not that we can write any program with a Turing complete language, but that we produce the same computational result, quite possibly by simulating the other programming environment, just as we might Greenspun Lisp into every other programming language.
So when discussing media, no we can't make a bamboo bicycle that has exactly the same weight and strength as a carbon fibre bicycle. But then again, we can't write an assembler program with the same number of lines as the equivalent Haskell program, so those differences can be hand-waved away. The point is that we can make bicycles out of either material, and knowledge of the material is different from knowledge of a specific tool that works the material.
I think your point is interesting, but I'm not convinced that my suggestion is leakier than comparing C to hammers. I stand by my suggestion that hammers are more like IDEs than programming languages, and that there is a very important distinction between IDE as a tool and programming language as a tool. I reject the latter.
To borrow another Perlisism, "The debate rages on: Is this metaphor Bactrian or Dromedary?"