That's like saying that everything you build with Lego is a pirate ship: To build anything with Lego, you first need Lego bricks. And if you already have those, then you can also build a pirate ship.

Turing completeness is defined on computational models, i.e. sets of instructions that you can use to build algorihms. Not on the algorithms themselves. If you can simulate a Turing machine using only the tools that your model gives you, then it's Turing complete. That doesn't mean that everything else you build using those tools is special in any way.