Recently, we've seen several kinds of doves, along with jays, blackbirds, mockingbirds, and more. The birds scrape clean the stuff, along with the seeds, discarding the skin of the seedpod. It appears that the birds either digest the seeds, or pass them directly through their digestive systems. Either way, the viability of eaten seeds is low. The strategy for seed distribution seems to be in the stickiness of the mixture.
Birds are messy eaters, and get food all over themselves.
The seeds may stick to the birds. When the birds fly away, the stuff dries out and falls off, or they clean it off later. Insects, such as ants, also play a role in the distribution. They eat the goo and the seeds drop on the ground. The seeds are not very hardy.