The Z3 was not a general purpose computer; it was a calculator that performed a predetermined sequence of operations that was written to its tape. It was remarkable for being all-binary in an era when differential gears and cams were very common in computing devices, and had some other advanced features. But the 1990s article that declared it Turing-complete is just silly. It would apply to every four-function calculator that supports rounding, and programming a computer like that is not just "impractical" - both the tape and execution time would grow exponentially in number of branches - but it is not the model that Turing proposed. The whole point of Turing's (theoretical) device is that a short program using the abilities of that device could perform unlimited computations; if you make the program length unlimited instead, that's a much less interesting model of computation.

The problem is that anything that gets into Wikipedia becomes ingrained in the Internet's collective mind, which then can't be changed.