The responability of the supplier is to present for his delivered parts the homologation certificate accoring to the EU Regulation regarding that specific part. And you shouldn't test it. Now here comes the "dancing and music part":
If you are homologating a new vehicle,you have to present at the homologation of the vehicle all the homologation certificates of every subsystem, and also you have to demonstrate that all the homologated parts work together as it is required in the EU Directives and Regulations. To make it clear I give you an example:
We made a trolleybus. The steering subsystem, with the steering pumps was made by ZF, absolutely according to EU Regulations, the traction electrical motor was made by UMEB, the air compressor system for doors and suspension by Ganz Air, all homolgated, and all these together went over the max. noise level of the trolleybus specified by the Regulations. So we had to figure out what to do, because everybody was fully covered with homologation papers and the vehicle still didn't comply with the EU Regulation for noise level. In such cases you should know from where to take the problem. We have good engineers, and they managed to reduce the noise level, and we went to homologation again.
I also agree that you can meet this kind of working style only at fairly little companies, not at big companies, where you have every departement very clearly stated.