Besides, any claim that goes into an advertisement gives you more leverage to argue for a high quality standard. Marketing people can help you understand which parts of the product they believe are most critical for impressing customers in the field, which helps justify the resources to test them. Your relationship to management dictates how well you will be allowed to do your job. Do what you can to make management understand and value your test processes, and especially your mission. The key thing with management is to track historical data about customers experiencing critical problems, then show them how a better process might prevent future mishaps.
People learn best from their own failures.
Your most important relationship is with the developers. This is the one that makes your job or breaks it. What the product is and how it works. How the product is intended to be used. What parts of the product are at greater risk of failure.