Arguing rights or wrongs is, to me, a rather needless point to press after the fact. However, in the case of the Korean War the answer is certainly 'yes'. The United States brought the issue before the UN Security Council and proposed intervention on behalf of South Korea by a United Nations task force. This was the UN Security Resolution 84. The resolution was passed with 7 votes of 'yes' and 3 abstentions. So, from the perspective of international law at least, the US intervention (or rather the UN intervention, but it was overwhelmingly US-led) was 'right', in that it was legal.

Source: http://en.wikipedia.org/wiki/United_Nations_Security_Council_Resolution_84