Put simply, the question is whether a municipality can charge money for providing the service of access to documents. There's no question that they can charge for the costs of copying, but what about the time and effort of the poor civil servant who has to dig up the requested files?
It is also beyond doubt that the national government may not demand money for access to documents, except for things like copying costs. However, the regulation that establishes that does not apply to other government entities. Fortunately, the Constitution says that taxes may only be imposed pursuant to a law, so the municipality's actions have to have a basis in a statute. The statute in question, the Municipalities Act, says that levies can be charged for services provided by the municipality. Under Supreme Court precedent, this means services that are not part of the municipality's public duty, and that can be related directly and predominantly to a private interest that can be individualised. (Sorry for the clunky translation, but I'm trying to stay close to the original.) The case in question was about the fire department, which was held to be part of the municipality's public duty, meaning that no levies could be charged.
From this, and from the command in art. 110 Constitution that the government should carry out its duties in public, it should be clear that access to documents is part of the municipality's public duties. However, the Court of Appeals reasons differently. They agree with the defendant-appellant Leerdam that, since this request was made for the benefit of X's business (the ruling doesn't say, but X appears to be some kind of media company), the private interest of X predominates, meaning that levies are possible.
The municipality had charged € 54 for copying and € 1082,40 for the research carried out by the civil servant involved. The odd thing was that this last charge would not have been imposed if X had asked to see the documents. But since they asked for copies to be sent, they got the whole bill. Since this distinction makes no sense, the CoA ends up agreeing with the Court of First Instance and leaves the bill at € 54. However, that is just a particularity of this case. At the end of the day, this ruling would allow Leerdam to charge everyone who makes an Access to Documents request for the time and effort of the civil service. (Unless it's an environmental matter, in which my beloved Aarhus Convention forbids "charges that exceed a reasonable amount".)
The CoA pointedly remarks in the end of its ruling that it did not take into account the Council of Europe Convention on Access to Documents of 18 June 2009 because the Netherlands has not ratified it yet. (In fact, they haven't even signed it yet.) This is of course the correct approach. However, I would still consider the result they reached to be a fairly implausible application of precedent. It doesn't take a CoE Convention to conclude that:
Article 7 – Charges for access to official documents
1 Inspection of official documents on the premises of a public authority shall be free of charge. This does not prevent Parties from laying down charges for services in this respect provided by archives and museums.
2 A fee may be charged to the applicant for a copy of the official document, which should be reasonable and not exceed the actual costs of reproduction and delivery of the document. Tariffs of charges shall be published.
Under current Dutch law, too, that is easily the more obvious conclusion.