In the early days of our involvement with ISO 13485, before I was assigned to regulatory issues, we were working with NB "X". I think that business relationship evolved from our owner knowing someone who used "X". We didn't know what we were doing in regard to NB selection or anything else, but things were going fine.
At some point in the course of business, a friendly off-hours discussion ensued with a regulatory specialist from one of our largest customers. We were surprised to learn that, at least in this person's view, "X" was reputed to be capable, but "easy".
He had no problem with that. Nonetheless this caused us to inquire among other contacts to corroborate the information, and subsequently to change to NB "Y", which was generally reputed to be "hard". The motivation on our part was to maximize the perception that we were serious about our compliance stance.
That's a form of customer influence.