Joe has absolutely correctly answered your question. Let me discuss why this argument is being made.
Part of what makes bridge so challenging is that unlike chess, it is a game of incomplete information (another part is that unlike poker, all 52 cards are in play). One of the goals of the bidding and the play is to pass enough information about your hand to partner that they can do the right thing (and hopefully not enough that the opponents can do the right thing).
"Blind" opening leads (where your side have not been in the auction, and where the opponents' auction has not been very specific) are the hardest part of the game - the best players in the world concede a trick (against "I can see all the cards" best) over 20% of the time on this trick alone.
A little bit of bridge information: first there's the auction, then the play. In the auction, both pairs attempt to find the best contract for them (or disrupt the opponents doing the same), by using meanings for bids. But the bid always has to be higher than the last, and if you win the auction, you then have to try to win as many tricks in the play as you contracted for in the auction.
This auction ended at 3NT (why, I won't go into, but there's a bonus for making it that you don't get with any lower bid). That means that the declaring side must win 9 of the 13 tricks in the hand to "make" the contract (and get a positive score); if the defence takes 5 or more, then declarer can't make it any more, and pays penalties for being "set". Making more than 9 (or less than 8) is worth/penalized more, but almost nothing compared to whether they get 9 or not. This is critical for all the explanation below.
Choosing what suit to lead is an art. Choosing what card to lead, once the suit has been decided on, is a matter of agreement, based on standards. So:
Having decided to lead a spade, "standard" is the K ("top of sequence"). It tells partner you have the Q and either the J or 10 (usually), and if she can't see the J on the board or in her hand, then either you have it and it's a trick or declarer has it and when she gets in, she can lead through declarer to neutralize it.
Why lead a spade instead of anything else? Joe explains that one clearly - to set 3NT, you need 5 tricks (3NT means "I'll take 9 of the 13 tricks"). Four spades (one will be won by the Ace) and the ♦K you hope is an entry are the obvious 5.
There are other possibilities, too: Declarer has 15-17 HCP, and dummy has 9-14. Your 9 means that partner could have as much as 7, and four of them could be the ♠A. Or the ♦A. Or she might still have a spade when she gets in with whatever trick she does have, and you get your 4 spades that way.
For the ♦K to be right and the ♠K wrong, partner has to have ♦AQxxx or better - so you're hoping for 6 of the 7-or-fewer points in her hand, instead of 4 (an ace) or 3 (a useful K) or 2 (the ♦Q and they don't have 9 tricks without playing diamonds). Plus there's a very good chance the ♦K will give up a trick, and it might be the ninth.
There's little to go on with 1NT-3NT, but there is a strong implication that a major suit (hearts or spades) will work better than a minor suit (clubs or diamonds). Because of the way the scoring system works, finding a major suit fit is a big thing, and LHO hasn't even looked for one - so they don't have one. They could very easily have a diamond fit, though, especially as you only have two.
So, you can see that the spade is so much more likely to work than anything else, especially the ♦K you'd hope is your entry to the spades. But on this hand, the player being discussed led the ♦K, and caught partner with ♦AQJxx. The ♠K would have let the contract make; the ♦K set it before declarer got in.
This is - deliberately - a wildly exaggerated example, one where 999 999/1 000 000 would do one thing, but there is a hand where the other lead is right; when the 1/1 000 000 person leads it and it's right, it's really suspicious. This leads the writer into the meat of the story, with less exaggerated hands, but "when a pair make leads that 99/100 players at this level wouldn't, a lot, and it works, a lot, what's more likely - they're imaginative, they know more than everyone else about math, or they know something about the hand they didn't get legally?" And then proceeds to show a large number of hands where this pair did exactly that.
And the site is called
Now the counterargument to this (which the player in question has of course used) is that the hands are cherrypicked; that the large number of hands where they made the normal lead were ignored, and the ones where the odd lead didn't work didn't get mentioned, because it makes the argument look bad. And that's a very legitimate point; so what is becoming standard is to look at every hand to see if it's "Normal: 90; weird that worked: 2; weird that cost: 4; weird that didn't affect the result: 4" or "Normal: 94; weird that worked 4; weird that cost: 0; weird that didn't affect the result (but could have with a different lie of the other cards): 2."
Now, another thing that came up (later) is that there was an oddity in the way the board was replaced after the auction. Some people came up with an idea that how it was placed was passing suit information. That, too, could have just been a coincidence, but the fact that they insisted on sitting N/S (in control of replacing the board) and that video of a different set of hands was given to a different set of people who were asked "where was the board placed?" and "what suit would you want to show?" without being told the suspected "code". When the results matched...