Rep. Devin Nunes, the California Republican and chair of the House Intelligence Committee, claimed Wednesday that “the intelligence community incidentally collected information about U.S. citizens involved in the Trump transition” between President Trump’s election and his inauguration.

Nunes then headed to the White House to brief Trump. White House press secretary Sean Spicer read Nunes’s statement at a press conference and called it “startling information,” implying that it justified Trump’s recent claims that Trump Tower was wiretapped on former President Obama’s orders.

The underlying reality is likely significant but far less exciting: That Trump transition staffers were picked up by standard U.S. surveillance as they arranged for Trump to receive standard post-election calls from world leaders.

If so, what Nunes was describing would not vindicate Trump’s claims, and would also be a separate matter from reported contacts by Trump associates with Russian intelligence officials before the election.

A key goal of the National Security Agency is to monitor the communications of foreign leaders and their staffs. As documents leaked by former NSA whistleblower Edward Snowden revealed, this includes the leaders of allied countries like German Chancellor Angela Merkel. Friendly countries in turn spy on us just as enthusiastically.

Meanwhile, world leaders try to speak to newly-elected U.S. presidents as often as possible during the transition period, first to congratulate them and then to get a read on the incoming president and to influence their views on global politics.

But Trump’s transition, as reported at the time, was extremely chaotic; the president-elect’s team apparently went outside normal procedures to arrange many such calls, an approach that involved many staffers and others in Trump’s orbit.

For instance, former GOP presidential candidate Bob Dole played a role in setting up Trump’s precedent-breaking call with Taiwan President Tsai Ing-wen. President Mauricio Macri of Argentina said that he spoke with Ivanka Trump during his call with Trump. Australian Prime Minister Malcolm Turnbull got Trump’s phone number from professional golfer Greg Norman. The governments of Japan and China found it difficult to build contacts within Trump’s transition team and spent a great deal of time trying to do so.

So what would truly be “startling” would be if the U.S. intelligence apparatus hadn’t picked up many Trump staffers speaking with foreign targets of surveillance. This also means that comments like those of Democratic Rep. Ted Lieu of California, who said on Twitter that Trump “officials were either talking to agents of a foreign power, or people suspected of crimes,” are not meaningful. The people with whom Trump’s transition team would be speaking would of course be agents of a foreign power, and there would be nothing wrong with that.

All that said, Trump absolutely will have a legitimate complaint if Nunes was correct when he claimed that “details about U.S. persons associated with the incoming administration with little or no intelligence value were widely disseminated in intelligence community reporting [and] additional names of Trump transition team members were unmasked.”

Privacy advocates have long been concerned about exactly this type of scenario. When the communications of U.S. persons are swept up in spy agency surveillance, their identities can be used in queries against intelligence databases, but must eventually be masked through a process known as minimization. However, many identifying characteristics remain available to intelligence agents, both before and after minimization, allowing the government to engage in something akin to spying on Americans without a warrant. Moreover, NSA staff may decide to unmask Americans’ identity on their own, or be asked to do so by their superiors. This almost certainly is how it was possible for anonymous “current and former U.S. officials” to know that Michael Flynn discussed sanctions against Russia with that country’s ambassador, and then leak it to the Washington Post.

The best outcome now would be for Trump to use his power as president to declassify anything he wants, and make as much information public as possible about this “incidental collection.” If in fact any surveillance was conducted on his transition team that was improper by the government’s own standards, he has the power to prove it. If it wasn’t, he owes it to the U.S. not to hide what happened behind the classification curtain. Moreover, releasing everything would be an extremely valuable education for the American public about how much the government collects on its citizens even when it’s following its own rules.

In a recent conversation at the SXSW conference with The Intercept’s Jeremy Scahill, Snowden explained in more detail how the communications of Trump or his staff could have been picked up — and why Americans should be concerned not about Trump’s vulnerability to such wiretapping, but about their own: