Did you ever wonder why the war with Soviet Union was called the Cold War?
You can divide war into two different classes- conventional and covert.
The Cold War was mostly a covert war. Both sides knew they couldn't have a conventional war, because of the risks of it going nuclear. So we didn't want Soviet soldiers fighting US soldiers- because that would make it it a conventional war- but of course, there was times when this did occur- therein the term deniablity.
In a covert war the US could legally provide assistance: money, arms, supplies, intel, etc to one or more factions at war- these factions can "belong" to the recognized national govt, or they can be insurgency forces [if the US does not recognize what "might" be a recognized govt by other countries]. Now, this could become illegal if congress passed laws prohibiting it or the UN passed resolutions prohibiting it (e.g. sanctions). Though it is possible for Congress to contradict itself by passing laws opposed to supporting any covert action and for Congress funding this covert action. It's also possible for say France to support UN resolutions for sanctions (Iraq) and violate this UN resolution by allowing it's companies to sell arms (see deniablity).
[In situation in which a UN resolution is not upheld by the security member, the legal power of the resolution become questionable. Another way of saying this is the US might have a interest in strenghtening an UN resolution by enforcing the resolution, but if other countries are actively undermining this resolution, attempts at strengthening it could be seen as unpractical & foolish.]