In a basic sense, this is true
Not really it's just wrong. The one approach that came from Western cultures is the scientific method which is both objective (to the maximum extent any human method has yet achieved) and universal which is why there is no such thing as Chinese, Canadian or Indian etc science there is just science because it is universal. As you alluded to the scientific method has often (including now to some degree) found itself at odds with western culture so I would argue that the scientific method is a product of western culture but not part of it.

Arguing that it is "culturally situated" is nonsense. While science has definitely impacted western culture it has also impacted every culture around the planet and today there are scientists in every continent from a myriad of different cultures. Your culture may impact which questions you want to answer with science but, if you are doing it correctly, it will not affect the knowledge you find and that's why it is both universal and acultural. Indeed, the universal nature of science means it is one of the few things that can bring people of different cultures to work together towards a common goal: to understand the objective reality that we all share.