As an operator you are responsible if you have your disc in the window. Whoever prepped it and presented it; it goes against you. The only way you can get round that if it is on hire (Long or short term) and the hire company take out your disc and put it through on their account. I run a fleet and I have some owned and some on contract hire and they all go through on my account. 
We had headlight aim issues and the recent change in criteria has helped that. However, some of our vehicles are prepped by service providers on actual test lanes they have on site. All vehicles go through a voluntary test before test and even then we have had a failure on brakes when it passed the day before, or a PRS on the headlamps (before change in criteria) when they were fine before. 
The contracts I sign up to have penalties for PRS or MOT failure and any instances need a written report from the SP to accompany the letter I’ll send to the TC; and if my vehicle gets a PG9 that can be attributed to the service provider’s work (e.g. Loose wheel nut the day after inspection) there is a penalty as well as a rollocking and they are responsible for the financial aspect and resource to present the vehicle to have the prohibition cleared.
I do not pay top dollar for this either and frankly wonder how some do it for the money I pay but if they are prepared to do it then we’ll go with it as long as the standard is what I require.
If they want your business and you are a good payer then there is no excuse for them to fall below the standard you require.