It does sound like they might have been doing what was called 'pursuit training' - with the BMW acting as the bandit car and the marked vehicle keeping up . They used to do this at Tulliallan , but I was previously told that this had been stopped because of danger to the public .
By the description given in the original post , it sounds as though the BMW executed a safe overtake , but the following driver ought to have held back - if on a training run , he would have been marked down for this - with only two in the car it would either have been an assessment drive or nothing to do with training at all : training runs are normally four to a car with one instructor plus three students taking turn about .
In the Fire Service , although we have our own ERDTU , we don't tend to get into real high speed stuff as the police do - appliance drivers are taught advanced techniques but are never going to do much more than normal traffic speeds in 20+ tons of fire appliance ; our officers are now issued with instructions forbidding any more than 20mph above speed limits on response drives and full compliance with limits at all other times .
Any incidents which are more than minor vehicle damage only ( dents , clipped wing mirrors etc ) are fully investigated , sometimes in conjunction with police , even the minor bumps involve lots of paperwork .
Thankfully , there have been very few injury accidents involving our vehicles ; I can only recall one in recent years where a MOP was injured , and a handful where our own guys were hurt .