We needed to keep the Suez in Egyptian hands to keep a modicum of peace in the region. As for Argentina, we did get involved diplomatically; and I am unaware of Margaret Thatcher ever seeking US military involvement, nor has she ever (to the best of my knowledge) been critical of anything President Reagan ever did.
"nor has she ever...been critical of anything...Reagan ever did."
In point of fact, Thatcher was utterly opposed to the invasion of Grenada. Thatcher telephoned Reagan on October 25, 1983, and urged him not to launch an invasion of Grenada. "Thatcher was unyielding in her opposition to it." (Martin Gilbert, 'A History of the 20th Cent.', Stoddart, 1999, p.600.)
There may be other examples of disagreements between the Iron Lady and the Ray-Gun. This is just one I was able to find in a minute's browsing in a decent history book.
I liked your coy reference to the U.S. being "diplomatically involved" with Argentina. Considering that the preferred educational establishment of the assassins and torturers of the Argentinian junta was the School of the Americas, this must rate as some kind of masterpiece of understatement.