I am not sure you know the meaning of inalienable. There is no right to publish prejudicial material to a trial because the publishers cannot prevent that material interacting with the trial. In theory if the publishers were able to effectively restrict access then they would not be restricted in publishing. As has been said (excepting certain reporting restrictions particular to a trial e.g. anonymity of minors and rape victims), reporting on the trial and evidence given therein is free.
This is an example of a conflict of rights, between absolute free speech (in this case being regarded as equivalent to shouting fire in a crowded theatre), and right to a fair trial. Because the latter may result in permanent loss of rights of an individual, temporary restrictions on rights of others are justified.
The right is alienated.