Interesting, but the article does say that it happened with the guillotine.
When the guillotine was first introduced, some condemned criminals would pay executioners to sharpen the blade, ensuring a quick and relatively merciful end. Prisoners sentenced to beheading in certain eras in England would also pay their executioners, requesting execution in a single blow. In both of these senses, the payment was more like a bribe than a specific fee for services rendered, as it were.