Actually, blockades have been legal as far as some countries and the U.N. has been concerned in the past, mainly to solve problems without the parties resorting to war, or as a way to provide economic pressure.
The legal status depends on who's looking at it. For instance, the Brazilian blockade of Río de la Plata in 1826, was lawful according to British law but unlawful under French and American law.
Therefore, it's possible that they've studied the law, and are a specific distance from the planet that's allowable, or they are looking at particular laws within the Planetary Republic.
You say that it's equivalent to a castle siege in Medieval times, but it's really not. A castle will run out of food eventually, but cutting off trade to a country or a whole planet will not starve them, most likely, unless the resources are very limited or unless that they are highly dependent on imports to survive.
Now, as to whether her people were dying, the transmission may have been designed to bring the Queen back so they could force her to sign something, instead of people actually dying. The aim was not starvation.
EDIT: Also, just going to drop this here, It's Chapter VII of the Charter of the United Nations, the section which deals with what the U.N. can do BEFORE they resort to force, legally under their charter.
Article 41
The Security Council may decide what measures not involving the use of armed force are to be employed to give effect to its decisions, and it may call upon the Members of the United Nations to apply such measures. These may include complete or partial interruption of economic relations and of rail, sea, air, postal, telegraphic, radio, and other means of communication, and the severance of diplomatic relations.
Article 42 Should the Security Council consider that measures provided
for in Article 41 would be inadequate or have proved to be inadequate,
it may take such action by air, sea, or land forces as may be
necessary to maintain or restore international peace and security.
Such action may include demonstrations, blockade, and other operations
by air, sea, or land forces of Members of the United Nations.
Countries have always had differing views on whether a blockade is legal, and that generally depends on if they believe the country being blockaded is the bad guy...or if they make money in trade with the country being blockaded or the blockader. It sounds mercenary. It kinda is.
Edit: I didn't address this point that others have: Does the speaker really believe that what they are doing is legal? Other answers here cover this!
