I'm a pricing actuary (not motor though) but having spoken with my colleague who's worked as a motor pricing actuary for over 5 years, I can assure you it very much is a combination of statistics, continual monitoring of the portfolio, market conditions and regulation.
More often than not, heaps of data feed a GLM (a type of statistical model) which after a few tweaks, will output a premium. In simpler cases, it is merely a multiplicative structure (e.g. base = 500, age relativity = 0.8, car type relativity = 1.9 to give a premium of 500 * 0.8 * 1.9 = £760 per year). Such relativities would usually be the combination of statistics + underwriting input.
Continual monitoring of the portfolio refers to the fact that if a certain segment of the book (e.g. middle-aged performance car drivers) begins to deteriorate, a rate increase may be applied upon renewal, taking the price elasticity of the premium into account too.
Regulation can have an impact on the premium, e.g. Ogden rate changes and the subsequent impact on periodic payment orders. How litigious a country is will also affect the premium dramatically.
Motor and travel are some of the most technically priced types of insurance you can buy. It is when you enter the territory of marine, financial lines and other specialty lines that you begin to see numbers plucked out of the sky.