Wrong.
On the 23rd April, nine days before the Belgrano was sunk, the British delivered a statement to the Argentinians making it clear that military action was not limited to the exclusion zone.
In announcing the establishment of a Maritime Exclusion Zone around the Falkland Islands, Her Majesty’s Government made it clear that this measure was without prejudice to the right of the United Kingdom to take whatever additional measures may be needed in the exercise of its right of self-defence under Article 51 of the United Nations Charter. In this connection, Her Majesty’s Government now wishes to make clear that any approach on the part of Argentine warships, including submarines, naval auxiliaries or military aircraft, which could amount to a threat to interfere with the mission of British Forces in the South Atlantic will encounter the appropriate response.
http://www.raf.mod.uk/falklands/an1.html
Argentina should have been fully aware that the Belgrano was at risk. If it wasn’t, that was Argentina’s fault and just another of the many errors it made in getting into a war it couldn’t run properly.