In arguementitive cases this is so, but in relation to incidents where the cyclist has complained about the driver, I dont think the situation would be like that. The cyclist would have to prove the driver was in the wrong.
That is the situation in UK at present, and the whole point of the petition is to get that changed.
Under presumed liability, the driver would be assumed at fault unless thay could prove otherwise. This is the situation in most European countries.
There is a misconception that this goes against the principle of "innocent until proved guilty", but that principle relates to criminal law, whereas presumed liability relates to civil law.
In civil law, judgements are made on the balance of probabilities. The DfT stats show that the cyclist is almosy always the injured party in collisions between cycles and motor vehicles, and research published a couple of years ago showed that the motorist is to blame in the majority of those cases. It is clear therefore that the motor vehicle brings almost all of the risk to the situation. Given this, it is absurd that the victim bears the burdon of proof in such cases, hence the calls for presumed liability of motor vehicles.
It is also arguable on a similar basis that the cyclist should be presumed liable in collisions with pedestrians.