I'd argue that this relates to species-specific strategies of seed dispersal, so the answer depends on which species you're asking about. Here's an answer for chili peppers, which I think illustrates how complex and idiosyncratic these strategies can be.
As I mentioned in this answer, the seedsavers' manual Seed to Seed has great info on most plants, including the genus Capsicum (chili peppers). They say to clean the seeds from the peppers, and then dry them thoroughly but not in direct sun.
The Tewksbury lab has done someone amazing work on Capsicum evolution and seed dispersal from a biological standpoint. As published in Tewksbury and Nabhan 2001 (behind paywall, but described well in this Science in the News article) Capsicum fruits have evolved specifically to be eaten by birds, who do not have the receptors that make the fruits taste spicy to us and other mammals.
Essentially then, what you're trying to do when you hand-germinate seeds is to mimic the process of the fruit being eaten and passing through a bird gut. Tewksbury and Nabhan found that seeds from fruits eaten by birds actually germinated at a slightly higher rate than their control group of hand-processed seeds. In contrast, seeds eaten by mammals (who in normal settings totally avoid these spicy chilis) were destroyed and did not germinate.
Seed dispersal mediated by birds and other animals is one way that plants can be motile.