It also seems to me to be unlikely that life would get around easily among planets, but you never can tell.
Life does not seem to have waited very long for a seeding event. Some people think life on Earth may have originated within 100 MY of liquid water existing on earth.
On the other hand perhaps transfer opportunities were more common in the early solar system, when planetary impacts were more frequent.
If life were to be discovered in anywhere else in the solar system, this issue will inevitably be brought up.
An important issue would be whether it is something transported from Earth by earthling space probes. However, recent transfers should be revealed by great similarities to Earth life (in DNA sequences, since they would not have much time to evolve great differences).
Earlier (pre-human) transfers (of bacteria or archaea) would have the opportunity (time, a few billion years) to evolve and radiate to different forms/sequences, obscuring any earthly relationships by adapting to their different environment.
A distinct genetic system, that distinguishing Earth life from life that actually arose on other planets would seem to be pretty convincing.
However, a similar genetic system (or parts of metabolism) might not be as convincing an indicator of related origins as one might think.
Some have proposed that early Earth life arose from a mash-up of randomly generated, interacting organic chemicals, making simple prebiotic chemical that became initial (and still in part around) metabolic pathways. The argument is that these initial pathways would arise naturally because they are thermodynamically favored in the environment in which they arose.