of course we have an assigned dept to handle complaints, and we also train them well. complaint handling isn't easy and can sometimes be stressful and feel unrewarding.
I just sold my company (thank god) and even though it was quite busy with 1000s of customers a year I left it with trip advisor 5 stars. Getting 4 or 4.5 stars is quite common but 5 isn't easy. For handling complaints we followed this formula:
1. Apologise
2. Say what you'll do to prevent the problem happening again
3. Offer something (we commonly skipped this step)
4. Apologise again using the phrase about "receiving a service below the standard you had a right to expect"
We avoided like the plague getting into a discussion of the actual reason for complaint because so often the complaint was unreasonable. But we followed the steps above anyway because Customer is King.
In the vast majority of cases using the above formula resulted in customers changing from complainers to fans. Why? Because people complain because they want you to feel their pain. There aren't many other reasons. This was shown in a big study using data from (I think) Continental Airlines years ago. It showed what we found time and time again - that complaints handled well led to complainers becoming not just neutral but strongly positive about your company.
I did hear though that people in my industry who dealt with Japanese market had a different problem - unhappy customers generally didn't complain to the company directly but instead told everyone they knew and spread poison. That's obviously much harder to deal with.
I don't think your complaint handling staff should feel stressed (unless your product or service is really awful or they are paid or treated terribly). Instead they should try to view the process as an intellectual challenge.
Hope this helps a bit.