That is correct, but the article explicitly addresses this point and argues that the evidence points to Lilienfeld producing a working transistor.

"Later, some people claimed that Lilienfeld did not implement his ideas since "high-purity materials needed to make such devices work were decades away from being ready,"[CHLI] but the 1991 thesis by Bret Crawford offered evidence that "these claims are incorrect."[CRA91] Lilienfeld was an accomplished experimenter, and in 1995, Joel Ross[ROS95] "replicated the prescriptions of the same Lilienfeld patent. He was able to produce devices that remained stable for months."[ARN98] Also, in 1981, semiconductor physicist H. E. Stockman confirmed that "Lilienfeld demonstrated his remarkable tubeless radio receiver on many occasions".[EMM13]"

For many things (computers, rocketry, aerospace, etc.) and different reasons, Germany in the years around the second world war, was a pretty bad place to get international credit for your accomplishments.