Attributing change in DV to IV manipulation: between-groups (control group) vs mixed-model (pre&post measure)
There's a short straightforward answer, and a more nuanced answer.

The short answer is that people were randomly assigned to the two groups. Any baseline differences between people will be equally likely to affect both groups. Will there still be differences? Absolutely. This is why researchers use statistical inference to rule out the possibility that baseline differences are responsible for the observed difference.

The more nuanced answer is that we can't be certain that the observed differences aren't due to these random baseline differences. In any experiment, there will always be noise that causes differences in the groups. When researchers use statistical inference, they aren't able to say with certainty that the effect was due to the manipulation. They are merely assessing the probability that random noise could account for the data. If the probability that random noise can explain the data is very low, then researchers claim that the manipulation had an effect. However, this is a probabilistic inference and sometimes the researchers will be wrong and the difference really is due to noise. Within-subject designs help remove some of this noise, but not all of it, because people change over time, even over the short timescale of a social priming experiment.