There is a general principle of copyright law that predates television that copyrighted works can only be performed or copied with the consent of the copyright holder, that is not medium specific.
So, the principle of praeter legem (i.e. that the law doesn't speak to the issue, so it is not illegal) does not obviously apply. There is a law. It just so happens that the relevant law is simply a general one, rather than a specific one. But, there is nothing inherently bad about having general laws and sometimes general laws are better because they are more flexible in the face of changing circumstances than specific laws.
As @gnasher729 notes in a comment, the licensing contract for the content in the archive ultimately controls. It could be that someone at the broadcasting authority is being more crabbed in their interpretation of how the licensing contract language applies to the modern circumstances than is really reasonable. But, it is also certainly possible that general language in the licensing contract is sufficiently clear to cause any reasonable person to conclude that it allows TV broadcasts, but not internet streaming on demand.
There are many very well founded policy argument that copyright law is too restrictive and too strong, and should, for example, have a shorter duration or smaller damages or allow use without permission at a government set price. But, there is nothing inherently troublesome about the fact that a copyright holder who bargained for a certain price for a certain kind of use of a particular TV show, for example, is entitled to a newly negotiated additional compensation if the licensee wants to make new uses of that TV show that weren't previously included in the original license fee.