In principle, diesel in a petrol engine will do much less damage than the other way round.
However, the problem with diesel is that (unlike petrol) it tends to self-ignite at high pressures (in fact, diesel engines don't need spark plugs). That is the reason why the AA vehicle engine was still running for a minute after the key was removed.
So, "thinning" the diesel might work (if it is not a big amount), however I must agree that it would be better to drain the tank. Also, diesel is "dirtier", so you probably will have to change your petrol filter.