Earth is still throwing rocks into space in modern times, a significant portion of what was once the island of Krakatoa is now in space. The force of the explosion is said to have shot rocks the size of houses into space.
As for seeding the solar system I personally think it's possible but improbable due to the fact that when a space rock hits a planet or moon at that speed, it is instantly vaporised and then rains down on the surface as microscopic glass beads, if it survives that then it's certainly comes under the heading of "Life - but not as we know it".
Life is a natural phenomena, it's chemistry that talks, like volcanos or any other natural phenomena life will emerge when and where the conditions are right for it to do so, for example the conditions on Mars may once have been right for life to emerge, but a thunderstorm will never emerge under the current conditions. Science is now pretty confident that one place where conditions are right for life to emerge are deep sea vents. So sure, the Earth might sneeze it's germs on other planetary bodies, but if those germs are to survive they will need to find the conditions where life can emerge and survive anyway.
The whole binary debate around panspermia is missing the point entirely, any sizeable and 'watery' rock floating in space, be it a planet, moon, comet will probably have some indications of microbial life either past or present. In fact the people who came up with the panspermia concept think that the idea of a unique point in space and time for life to emerge is just silly, panspermia is more analogous to pollen floating through a field of wheat, the point being that the wheat itself is created from countless seeds.