The problem is that in Norway (like in most other monarchies), she only needs the permission of the Sovereign. Given Harald's own history with a father who refused to give permission for him to marry for many years, it seems he is rather 'soft' in this issue and decided that he will support his children in their choice of partners no matter what...
Personally, I think a system in which parliament has to approve a royal marriage is preferable over the one in which it is only a close family member deciding.
In Belgium, the constitution says that the King gives consent to marriages of people in the line of succession (hereafter referred to as "royal marriages"), but consent is declared by means of a royal decree which must be countersigned by a responsible minister. So, in practice, the person who gets married needs the dual consent of the King and the government.
On the other hand, the monarch must give his/her consent to a royal marriage in a meeting of the Privy Council in the UK or a meeting of the Council of State in Denmark. So, in accordance with the constitutional practice in those countries, it is implied that consent is granted by the King/Queen in Council, rather than the King/Queen personally, therefore also with the consent of the government.
The Act of Succession in Sweden says in turn that consent to royal marriages is explicitly given by the government, but the government can only give its consent upon a request by the monarch. So, again in practice, dual consent of the monarch and the government is required.
The Netherlands and Spain are the only European kingdoms where Parliament is explicitly involved in the process. In the Netherlands, consent must be given in the form of an act of Parliament passed in a joint session of the two houses, but a bill to that end must be introduced exclusively by the government on behalf of the King/Queen, so pre-approval by the government is needed. Spain, on the other hand, is somewhat odd because the Spanish constitution of 1978 does not explicitly require official consent to marriages of people in the line of succession, but the constitution allows the monarch
and the Parliament to jointly
forbid such marriages, in which case the person who gets married and the future descendants of the marriage lose their succession rights if the marriage takes place despite the prohibition. The important point though is that neither the monarch nor the Parliament can individually prohibit a marriage; the prohibition is legally binding only if both the monarch and the Parliament agree to it.
I am aware that King Harald V has declared in the past that he personally interprets the Norwegian constitution as vesting the power to consent to marriages of princes of the royal house in the King alone. However, even though the Norwegian constitution, unlike in Denmark and unlike in British law, does not explicitly say that consent must be given "in Council", I still feel that the King's interpretation is at odds with Norwegian constitutional doctrine. I say so because it is currently implied that all references in the constitution to official acts of "the King" are interpreted as acts of the King in Council. In any case, I don't think the King could realistically consent to a marriage despite an advice to the contrary by the government without triggering a constitutional crisis in practice.