Whatever your role, you are responsible for customer satisfaction.
In just about every position I've had, the first rule taught during the on-boarding process is that "it's not my job" is a forbidden phrase. If a customer asks you for something outside of your job description, your responsibility is to pass along that request to whomever is responsible.
I can guarantee that, someday, you will receive a call from a customer asking about something you know falls into a coworker's ballpark. The customer doesn't know this - they just know that you're the one who answered the phone and that you represent the company with which they have an issue.
They expect you to help them. The expect a positive support experience.
I work with WordPress, and I absolutely love it. Unfortunately, WordPress isn't perfect so every single client site I support uses at least 1 custom theme and at least 3 different plugins. More often than not, these plugins are created and maintained by a third party.
A third party I trust, but still not by me.
When one of these plugins break, my client's site breaks. She will then call me and say "hey, the site's broken! Please fix it."
If I were to say "yeah, that's because ______ isn't doing something right. You should contact the plugin vendor instead" I'd be out of a job. Instead, I say "oh, sure, I see what's wrong. Let me circle back with the development team and get everyone working on a fix."
Sometimes this involves a Skype ping to a fellow developer at another shop. Other times a cry for help on Twitter. In some, albeit rare, occasions it involves me forking the plugin to maintain a patch.[ref]I do always make efforts to push the fix upstream. Sometimes through a patch contributed on the plugin's Trac. Sometimes through the WordPress.org support forms. Sometimes through a GitHub pull request. Sometimes through an email to the original developer.[/ref]
What Is Your Role
Honestly, I don't care what your job title is. Whether you're an intern, an engineer, a senior designer, or a c-level executive the bottom line is that you deal with customers - even if only indirectly.
Your decisions, your level of effort throughout the workday, the quality of the work you produce - all of it impacts your customers' satisfaction (and their willingness to keep paying you money rather than your competition).
Even Steve Jobs at Apple understood this:
Jobs even got directly involved in customer service, which was a part of Apple's business for which he exercised a great deal of attention and patience. He fielded e-mails about broken laptops and intervened on support calls.
Similarly, Automattic (probably the foremost WordPress company) requires all new employees to partake in a 3-week support rotation upon entering the company:
Automattic developed a 3 week support rotation to help ease in employees to get accustomed to working remotely. This support rotation helps new employees to meet established employees immediately, also gets them familiar with the communication methods. It also provides the opportunity to see what their customers are dealing with, to see what their problems are that they’ll be helping to solve.
While these two examples are examples of direct customer support, hopefully you understand the emphasis both companies have placed on every position's impact on customer satisfaction.
At the end of the day - customer satisfaction equates to the level of sustainability in your business. If, in your role, you're not fighting to keep your business sustainable ... what are you working for?