In cases like these, the product could be completely cruelty-free or the status of the ingredients could be questionable. It depends upon the company.
For example, both Bath & Body Works and Aveda use similar statements on their packaging, and neither company tests ingredients on animals. This statement is often used to meet language requirements when products marketed in both the U.S. and the U.K. use the same packaging in both countries.
Since most ingredients have been tested on animals by someone at some time in the past, England does not allow a company to include phrases such as “no animal testing” on its products, even if that company has not conducted animal tests on its ingredients.