"true experiments" are studies where the experimenter can determine, usually through a random process, which participants get the treatment (e.g. name introduction in Garrity and Degelman tipping study) and which participants are in the control condition (no name introduction).
Since the only systematic difference between participants who get the treatment and those who are control participants is the randomly assigned treatment, the E can be confident the treatment caused any statistically significant differences that show up on the dependent variable. Recall that statistically significant means that the results show there is a systematic effect of the IV on the DV. True experiments are so valuable because they make sure the only systematic difference between the participants in the experimental group and those in the control group is getting the treatment or not. So the logic is if the statistics show there is a significant difference in the DV values between the experimental and control group, the only explanation for it is the treatment caused it since except for the treatment the only differences between the experimental and control group participants are chance, accidental differences.
Statistics are used to see if there is a real difference to be explained or if the difference is an illusion and could be explained by chance. Since people are variable in their responses and any one study will have only a small group of people, called a sample, statistics let us make probability judgments or likelihood judgments that the observed difference or relationship in our data would be found in replications of our study and therefore expect to find the same result in the population. If we think chance is not an explanation for our results we would say the results are statistically significant.