Grammar

Placebos themselves don't do anything. What's significant is the effect that taking them can have on certain people with certain medical problems in a certain settings, in a specific time.

Q) I was wondering if the "... that taking them...." part should be "... that takes them...." Am I right? If not, why so?

Oh!!!!!!!!!!! Eureka!!~

I'm sorry but I just understood why is the original is correct. I didn't understand even after 'd seen that sentence several times before I post this thread, but after checking out the translation in my language, i got the point.
In "...that taking them...," taking is the subject in the that clause.