Do your best to solve the problem or lead the customer to the right specialist and make sure that she is happy with everything. Otherwise, you give an impression that the internal structure of the company is much more important than the customer's needs.
Does it have to be taken so seriously all the time? For instance, when developers are asked about the pricing, it is unlikely they answer something other than "I don't deal with that". Situations are indeed different. Naturally, the customers themselves understand that it's not like every employee in the company can figure out everything. Nevertheless, a bad aftertaste remains: they did not help, did not do anything special — only followed the rules.
A great role model is a seller in this regard. They rarely give up and do the impossible to achieve a result. When another deal comes in and the customer asks for something that the salesperson can't do, the latter starts to "shake" everyone around, from the cleaning lady to the director, to do everything in the best way possible.
Of course, sellers have a personal interest in customer satisfaction, as they receive commissions after sealing the deal. Unlike them, support agents do not sell products or services directly. However, the profit of the company is highly dependent on how well they perform their duties.
Let's look at three examples. Customers come to the wrong place in each of them.