In journalism as in science, proving a negative is notoriously difficult. Recent attempts to knock down speculation that the Vatican has vetoed several potential nominees for U.S. ambassador to the Holy See make the point in especially clear fashion.

The rumor mill cranked into motion with an April 2 piece from Newsmax quoting Italian journalist Massimo Franco, author of a recent book on U.S./Vatican relations. Franco asserted that several pro-choice Catholics have been floated as Obama’s Vatican representative, only to be rejected by Rome as a way of drawing a line in the sand. (Under international law, a state is free to reject anybody it likes as an ambassador.) The story was then picked up by the Washington Times and other news outlets in the States, as well as by the Italian media, often citing unnamed Vatican sources.

Lending the story sex appeal is the fact that one of the names allegedly drawing a “thanks, but no thanks” has been Caroline Kennedy, the high-profile daughter of John F. Kennedy.

Usually, the second or third graf of these stories suggests that the stand-off is symbolic of deteriorating relations between the White House and the Vatican, in light of the Obama administration’s pro-choice decisions to reverse the Mexico City policy, to liberalize federal funding for embryonic stem cell research, and so on. As several Italian analysts have put it, the Vatican’s fear is that Obama will become a “planetary Zapatero” – referring to Spain’s Socialist Prime Minister José Luis Rodríguez Zapatero, the grandson of an anti-clerical revolutionary, who has challenged the Catholic church on virtually every conceivable cultural front.

Last week, the Italian paper Il Giornale carried an article signed by Andrea Tornielli, a well-connected Vatican writer, asserting that “at least three names – but some say it’s even more – have been ‘burned’ before the proposed nomination could even be formalized, because they are ‘pro-choice’ on abortion.”

Officially, the Vatican says these accounts are hooey.

On April 9, Catholic News Service, the agency of the U.S. bishops’ conference, moved a story citing the Vatican spokesperson, Jesuit Fr. Federico Lombardi. “No proposals about the new ambassador of the United States to the Holy See have reached the Vatican, and therefore it is not true that they have been rejected. The rumors circulating about this topic are not reliable,” Lombardi said.

Informally, some Vatican diplomats have groused that these stories are “all lies,” a typical example of Italian journalists penning romanzi (novels) rather than facts. One senior Vatican official told me April 13 that there are dozens of ambassadorial positions all across Europe that Obama has yet to fill, so why should anyone make a big deal out of the fact that the representative to the Holy See hasn’t been named?

The frustration in this official’s voice, reacting to the stories of diplomatic brinksmanship, was audible even over a long-distance phone line.

Privately, officials note that these reports have circulated mostly in conservative news outlets with an interest in stoking conflict between the Vatican and the White House. This is an especially tempting hypothesis in light of the mounting polemic over Obama’s scheduled May 17 commencement address at the University of Notre Dame. Pro-life critics would like nothing better than to be able to cite a Vatican snub of the administration.

Those inclined to take the reports seriously, on the other hand, regard Lombardi’s April 9 comment as a classic “non-denial denial.” Lombardi said no “proposals” had reached the Vatican, they note, leaving open the possibility that less formal trial balloons may indeed have been floated and shot down.

So, what’s going on?

To some extent, I suspect it’s semantics. Several weeks ago, before the recent cycle of reporting, I had a conversation with a senior Vatican diplomat. In passing, I brought up the possibility that Obama might name Pepperdine law professor and former White House counsel Douglas Kmiec, who became a lightning rod during the 2008 campaign by arguing that pro-life Catholics could support the Democrats. This diplomat’s response was, “I think Obama is wiser than that.”

Was that an informal veto? Or was it just two guys talking?

That’s what makes proving this negative so hard. Inevitably people have been speculating about the ambassador’s job, and some of those speculating have been Vatican officials. Their off-the-record opinions have become part of the media drumbeat – even if they fall well short of expressing the official position of the Holy See in response to a formal request for agrément, meaning the acceptance of a proposed ambassador under the Vienna Convention on Diplomatic Relations of 1961.

At the end of the day, the recent flurry of press accounts probably tells us relatively little about who will eventually move into the Villa Richardson (the residence of the U.S. ambassador to the Vatican). It does, however, illustrate an important point: Relations between the Obama White House and the Vatican are reaching a crossroads, and the choice of an ambassador will be read as a signal of which way the president wants things to go.

So far, the Vatican has kept its distance from the most strident anti-Obama sectors of American Catholic opinion. Many Vatican officials (except, perhaps, the Americans) are favorably inclined toward much of what Obama represents – his multilateralism in foreign policy, his positions on immigration and poverty relief, and his opposition to the Iraq war.

For example, Vatican diplomats appreciated Obama’s recent support for increased aid to developing nations at the recent G-20 summit. One senior Vatican official also told me Monday that the Holy See has been “encouraged” by early signals about the administration’s approach to the Middle East, including its willingness to talk with Iran and its reiteration of support for a two-state solution to the Israeli/Palestinian conflict.

If the eventual reading in the Vatican is that Obama is not Zapatero – meaning that the president is not motivated by some cultural baggage to seek conflict with the church –collaboration on several fronts seems within reach. By both training and instinct, most Vatican diplomats regard the idea that the Holy See should shun the Obama administration tout court as partisan politics rather than gospel witness. (Case in point: several Vatican diplomats with whom I’ve spoken have no problem with Notre Dame inviting Obama to speak, though they would draw the line at offering him an honorary degree.)

Yet the Vatican is also loath to be seen as undercutting American bishops, or as “winking” at the administration’s pro-choice policies.

As a result, Obama’s choice as ambassador will have huge symbolic importance. For those who believe it’s a good thing for the world’s leading “hard” and “soft” powers to be on speaking terms, the sooner the administration can name an ambassador likely to bolster the prospects for dialogue – meaning, to be blunt, someone who isn’t seen as a “Zapatero Catholic” – the better. If the administration fails to have such a person in place by the G-8 summit in Italy in July, all bets may be off.

In the meantime, however, the message coming from the Vatican seems to be to take what you read in the papers with a grain of salt.