Argentina knew that if the British fought, that Argentina would lose.
Especially as it was an unspoken truth that if the British got in trouble, the U.S. would send a carrier battle group and win the war for them.
But the thing is, the US had no interest in helping in this particular case. Better have the British knocked down a peg or two, and get rid of that (to the US) strategically worthless island cluster that would always hobble Britain's credibility due to its immense vulnerability.
And as said, the Royal Navy was almost incapable of taking back the islands, amounting to very
little more than this "corrupt police force" you speak of. Without US help, there would be no reconquest unless the intrepid
and the Fearless
could sail; and if they couldn't sail, there certainly wouldn't be US help, as this "British" operation would cease to be a British one...
The U.S. helped the British massively in any case with fuel, weapons, munitions, intelligence, et cetera.
No way the U.S. would ever have allowed the British to be embarassed.
If for no other reason, the U.S. needed British support in their hard line in Europe with the Soviet Union. In particular the coming deployment of 572 nuclear missiles to be deployed in Western Europe in 1983 (including 100 or so in Britain).