Except apparently in the case of the explanation of rabbit's blood on the silencer?
As Cliff says a hollowpoint bullet is very effective and a rabbit or rat will normally be cleanly killed if hit by one. However if the shot is badly placed (normally with a rabbit a head shot is taken so accuracy is important) the animal can be left incapacitated but still alive. It then needs to be dispatched quickly and humanely. There are different ways of achieving this but a second shot as close range is possible.
We should remember here that the quantities of blood we are talking about are very small. They were not necessarily deposited on and in the silencer at the same time. A likely source of blood contamination is by transfer from the shooter himself. For example a rabbit or rat of fox is shot, the body is then picked up by the shooter, who continues to handle the rifle and sound moderator. If the sound moderator is dismantled to clean or check for fouling of the baffles the components have to be handled by the shooter.
When the sound moderator was dismantled by the police before it was forwarded to the laboratory there was a further opportunity for contamination, particular if (as seems likely) the sound moderator was handled on the same bench or surface as the rifle.
