Front line staff members have to deal with "hot topics." These are things like collection challenges, rowdy kids, people looking at inappropriate web sites, and defensive questions about library budgets, millages, or non-resident fees (to name just a few!). Having a policy is crucial for dealing with any hot topic, but should be used as a "back pocket" method.
Most often, patrons just want to be heard. Listening to them and sympathizing with their situation is sometimes enough. There is no need to bring up policy and be defensive about why the library operates a certain way. The more calm and reasonable the staff member is, the more the patron will be too.
Compromise is important. Patrons who demand resolution may be perfectly fine with a compromise. Maybe a reference book cannot be checked out, but the library could offer some free photocopies out of the book. Maybe a computer class is full, but a librarian could offer a shorter one-on-one appointment with the patron. Maybe a popular DVD is inappropriate by the patron's standards, but a list of titles suitable to their tastes can be provided. In these examples, there is no need to bring up library policy, provide forms to be filled out by the patron, or bring the library director into the discussion. Everyone got what they wanted.
Of course, there are people in the world who have no interest in compromise. Those are the situations when policy, forms, and library administrators should be brought in. My stance here is that they are a last resort. Kindness, compassion, and understanding go a long way toward appeasing patrons who just want to be heard and taken seriously.