Here's his exchange with "Fox and Friends" from Thursday morning:
BRIAN KILMEADE: Clinton campaign says this is a national security issue. Now, the idea that you'd have any American calling for a foreign power to commit espionage in the U.S. for the purpose of somehow changing an election, I think that we're now in a national security space. Your reaction?
TRUMP: You have to be kidding. His client, his person, deleted 33,000 emails illegally. You look at that. And when I'm being sarcastic with something —
KILMEADE: Were you being sarcastic?
TRUMP: Of course, I'm being sarcastic. But you have 33,000 e-mails deleted, and the real problem is what was said in those emails from the Democratic National Committee. You take a look at what was said in those emails — it's disgraceful. It's disgraceful. They talk about religion, they talk about race, they talk about all sorts of things, including women, and what they said in those emails is a disgrace.
Trump backer and former New York City mayor Rudy Giuliani offered the same explanation later on CNN: "No. He was telling a joke. When he got off the plane, he tweeted out the emails should be sent to the FBI. He was joking around."
Here's why this sarcasm explanation doesn't hold water:
1. Trump campaign officials never said he was joking on Wednesday
They mounted a robust defense, mind you, but they didn't say it was a joke.
They said he never technically advocated "hacking" into Clinton's emails. They said he was merely urging Russia or anybody else to turn over the emails to the FBI — not use them for espionage. They accused Democrats of seizing on this to try to change the subject from the leaked DNC emails.
Trump's defenders on social media and elsewhere did suggest he was joking — including Newt Gingrich.
But that wasn't the line from the campaign — or even one of its multiple defenses.
In a tweet after the comments exploded on social media, Trump sought to explain a little bit — apparently suggesting he simply meant that the emails should be turned over to the FBI "if Russia or any other country or person has" them. Again, no mention of joking around.
If Trump was just joking, this would have been a good time to say that. Instead, he doubled down on the idea that this might be a good thing because the emails could be kindly shared with the FBI.
This wasn't a one-off quip in Trump's news conference on Wednesday. He initially said he hoped the Russians had the emails, and then he returned later to say that if they didn't have them, he hoped they would obtain them.
First: "By the way, they hacked — they probably have her 33,000 emails. I hope they do. They probably have her 33,000 emails that she lost and deleted because you'd see some beauties there. So let's see."
Later: "Russia, if you're listening: I hope you're able to find the 30,000 emails that are missing. I think you will probably be rewarded mightily by our press. Let's see if that happens."
You can look at the video for yourself below and try to deduce whether he was, in fact, having a laugh. To say it once and then return to it later suggests it was a message he meant to deliver. Even if he was joking about wanting Russia to get the emails, was he also joking about hoping Russia already had them?
4. A reporter gave him an out -- that he didn't take
NBC's Katy Tur, later in Wednesday's press conference, basically asked Trump twice if he was serious. In response, Trump indicated he had no qualms about, in Tur's words, "asking a foreign government — Russia, China, anybody — to interfere, to hack into the system of anybody's in this country."
NBC News reporter Katy Tur surely spoke for many journalists when she followed up that surprising statement with a question: "Do you have any qualms about asking a foreign government — Russia, China, anybody — to interfere, to hack into the system of anybody's in this country?"
"That's up to the president," Trump replied.
Um, yeah. And you want to be the president, Donald Trump. The question was whether it is responsible for you — a person who wants to be president — to promote Russian hacking.
Trump didn't want to talk about that; he wanted to talk instead about how Vladimir Putin "has no respect" for the current president. Tur tried to steer him back to her original inquiry and asked again, "Does that not give you pause?"
"No, it gives me no pause," Trump said. "If they have them, they have them."
5. He's mentioned it before
One thing that escaped notice in some of the coverage Wednesday: This isn't even the first time Trump has waded into the idea of foreign powers obtaining Clinton's emails. In fact, last month he said he thought "our enemies" already had them.
"While we may not know what is in those deleted emails, our enemies probably do," he said, without citing any evidence. "So they probably now have a blackmail file over someone who wants to be president of the United States. This fact alone disqualifies her from the presidency."
So no fewer than four times now has Trump alluded to the idea of a foreign power getting Clinton's emails. He has made a steady progression on this from "they have the emails" to "I hope they have them" to "if they don't, I hope they get them" to "if they have them, they should turn them over." This suggests it's an idea he's decided he wants to press. Maybe one of the comments could be construed as a joke, but all of them?
And again, most importantly: The Trump campaign's official responses to the controversy on Wednesday made no mention of a joke. The campaign instead argued semantics and said the issue was being politicized.
If it's all just a joke, Trump might want to work on his delivery.