The lack of accidents and crime are more likely related to a general trend in crime going down from before they started turning off the lights.
There's lots of room for methodology errors. Here's another:
Comparing murder rates between Great Britain and the US is complicated by differences in reporting. The US bumps the murder stat when there is a body and evidence of foul play. G.B. bumps it when they have a conviction.
Do they do that with other crime? If so, stable stats in the absence of street lighting might mean that any rise in crime is compensated for by a fall in identifying, apprehending, and convicting the criminals responsible. (Indeed, turning off the lights might easily result in LOWERED crime statistics at the same time it was causing a drastic increase in actual crime.)