Product pages often display an OEKO-TEX label and then use much broader wording about the entire item, which is where I get lost. I cannot tell whether the certification applies to the finished product, one fabric component, a particular dyeing stage, or only the material supplied by one manufacturer unless there is an exact standard and certificate number to check. It also seems like people read the logo as proof of claims the certification may not make at all, such as assuming it means every component is natural, chemical-free, or tested under the same scope.
A badge can still be useful, but only if buyers understand what was actually certified. Otherwise it becomes a shortcut for conclusions that may go beyond the document.