The Secretary of State wanted the withdrawal of "all foreign forces" from Lebanon - a reference to the Syrian army (which the Lebanese authorities accept, however grudgingly) and the Israeli army. She wanted "calm" in southern Lebanon - which would allow the Israelis a comfortable occupation until they carry out their promised withdrawal - and she asked, for the first time, for the extradition of Lebanese who staged four anti-American attacks during the civil war. These included the murderer of the US ambassador in 1976, the hijackers of a TWA passenger jet in 1986, the killer of an American passenger on the plane and those responsible for the suicide-bombing of the US Marine base in Beirut in 1982.
Mr Hoss patiently explained that the Syrian army had been invited to Lebanon in 1976 by the president at the time, Sulieman Franjieh, and the Syrians would stay as long as the Lebanese authorities wanted them to - albeit that the Beirut government is scarcely in a position to ask its Arab "sister" with its 22,000 troops to leave.
The Lebanese supported the "resistance", Mr Hoss told Ms Albright and while he regretted the deaths of Americans in wartime Lebanon, they took place "in a tragic epoch" upon which Lebanon wished to turn the page.
Ms Albright was not going to get the extradition of the men who hijacked the TWA flight or bombed the Marine base who, as she well knew, are also responsible for attacks on Israeli occupation troops. Indeed, that may have been the real reason for her request - there were, after all, plenty of other Americans killed in Lebanon upon whose fate Ms Albright did not dwell.
But what took the Lebanese aback was her reference to the more than 200,000 Palestinian refugees in Lebanon - survivors or children or grandchildren of the 1948 expulsion from what is now Israel. This was a "sensitive and intricate matter," she said and it would be difficult to imagine the Israelis allowing any of these Palestinians returning to their former homes. It was a matter, she said, for the refugee commission set up in 1991.
All this was being said by Ms Albright, remember, months before the refugees' fate is supposed to be decided in Israeli-Palestinian final status talks.
Mr Hoss saw the trap at once. Lebanon does not want hundreds of thousands of Palestinians "implanted" in Lebanon. And, he said, the 1991 commission had nothing to do with Palestinian repatriation - only to do with living conditions of refugees in their camps.
Was Ms Albright, one wonders, ignorant of all this? Or was this an attempt to write the Palestinian refugees in Lebanon off the negotiating table? It's not difficult to see why it might be the latter.
Israel's Prime Minister, Ehud Barak, has stated clearly that the three and a half million Palestinians in the diaspora can never return to the lands they once owned in what is now Israel. He will leave Jewish settlements in the West Bank and Gaza. Jerusalem will never be a Palestinian capital. He now talks not so much of an Israeli withdrawal "from" the occupied Syrian Golan Heights - the only way in which Israel will achieve peace with Syria - but "on" the Golan Heights, which is not the same thing.
Yasser Arafat - who "will sign any piece of paper put in front of him", as a Lebanese who knows him well put it this week - is now being presented with a village as his new capital: Abu Dis, a few hundred metres from the city walls and the Muslim shrines.
East Jerusalem, with its Israeli extensions, now has a substantial Jewish majority. Palestinian residents are still losing their identity cards as the Israelis claim they are no longer "resident" in the city they were born in. Palestinian cynics in Lebanon suspect that Mr Arafat will eventually accept Abu Dis with "access to the holy places" thrown in as compensation so that he can honour his promise to "pray in the Al Aqsa mosque".
There might be 14 borough councils in Jerusalem, six of them Palestinian and flying Palestinian flags, the rest Israeli and with Israel still controlling the entire city.
It sounds a miserable end to the 1993 Oslo agreement, but a predictable one. The refugees in Lebanon might be encouraged to live in a crowded West Bank - under the terms of family reunion that have apparently already allowed 120,000 diaspora Palestinians to move to PLO-controlled territory - or in the suffocating slums of Gaza. Otherwise, they will be left to rot.
The massive Jewish settlements will stay in the rump and divided state that Mr Arafat will feel unable to resist declaring. Jerusalem will be open to Palestinian worshippers via a "Danzig" type corridor from a village that will be called a capital. And the refugees in the middens of the Lebanese camps can forget their "right of return".