Agreed, but this study was specifically designed to highlight the problem not solve it. And the results would be useless, or non-existent, if they restricted themselves to scientists that would co-operate fully with the process and the possible "shaming" afterward.
You might be being a little harsh. There is a huge difference between "hey, I'm having a problem reproducing your results, want to help me either reproduce or disprove your results?", which legitimate scientists will and do participate in, and "I'm doing a study on unreproducible results and want to publish your paper and name in the list afterwards".
Notice they say they got help without the shaming part so the scientists were willing to participate, just not get listed.
I personally know scientists who have helped out with disproving their own findings, it's not uncommon.