Regardless of whether or not they have the infrastructure to respond, here are some ways to look at it:
1. Is the feedback legitimate? There are many instances where the negativity actually has some merit. It's hard for everybody to have a pristine experience when issues pop up. In a lot of instances, the negative feedback is not about the overall work quality or efficiency, but is an exception to the rule. If the negative feedback is legitimate, it does require some kind of response. Does it require a personal response in every instance? Not necessarily. As long as the response is communicated in a human and personal way and mutually agreeable it could correct the course.
2. Is the person crazy? Don't laugh. It is possible. We've all read peer reviews and marvelled at how someone's review of a work package has no real attachment to the reality we all share. The world is full of crazy people who are just looking for a soapbox to be heard or a cause to take on. In this instance, you have to tread carefully. Responding may open up a can of worms that will see no end and no reason. No responding might only aggravate the individual. These are special/case-by-case instances, and they might require something more traditional - like a phone call - to try and resolve the scenario. If you get a mixed bag of Positive and Negative feedback very frequently from the same person, it just time to re-think your strategies.
3. Is apologizing an option? Apologies definitely go a long way. But be political and dont give away too much!
4. Should you just forget about it and move on? There are many schools of thoughts on this. Some people say you have to respond to each and every piece of feedback (both positive and negative), some argue that you should only respond to those who really do have some kind of impact, and then there is the group that simply sits backs and just lets it fly without ever responding. Your mileage may vary. Depending on the scenario, the type of feedback and the voices behind the noise, is how you will best gauge how to respond. It is usually good to respond in some kind of fashion so that your own POV (point of view) is - at least - a part of the conversation.
5. Should you respond to everything? It's very easy to respond to the good stuff, it is hard (and time consuming) to respond to the negative by citing justification and stuff. The answer to this one ties into #4. In a perfect world, yes - respond to everything (with the exception of the people in #2). In responding, you're not just answering to this one individual's gripe, you're better able to reflect on how your brand "lives" in people's minds, and I believe this will make you a better Marketer, a better Communications Professional and a better brand.