Rita's a snake
In a 2007 wrap-up chat for Bloomsbury, Rowling gave a frank assessment of Ms Skeeter's veracity:
Is [R]ita [S]keeter still reporting[?]
Naturally, what could stop Rita? I imagine she immediately dashed off a biography of Harry after he defeated Voldemort. One quarter truth to three quarters rubbish.
Her story on Hermione drugging Krum, Potter, & al. with love potion was based on accounts from Pansy Parkinson but not otherwise supported by the text (HP&GF).
but not necessarily wrong here...
She has a legitimately true account of Dumbledore somewhere thanks to having drugged the historian and Dumbledore-family friend Bathilda Bagshot with veritaserum (HP&DH). The majority of her known articles deal with real events, retold salaciously.
A big theme of the Potter books, though, is how everyone was dishonest to the children 'for their own good' and adults who looked like saints and heroes are, after all, just human. Where they have become selfless, it's very often because of a need to atone for great earlier mistakes.
Egbert the Egregious seems to have won the wand in an actual duel (Tales of Beedle the Bard) but that's based on medieval lore. The wording HP&DH uses ("the wand came... after... slaughter") actually implies usurpation in the usual way: murder or sneakiness.
Similarly, the only in-universe 'proof' of the great duel is the very unreliable testimony of Dumbledore's school chum and fanboy Elphias Doge. It's possible Riddle helped (playing the role of the atomic bomb in the WWII analogue); it's possible Dumbledore scored a cheap shot (ditto); it's possible he talked a still moony Grindelwald into feeling sorry about the deaths of Dumbledore's family members and all the other wizards being harmed 'for the greater good'; it's even more probable he used some reunion and guilt to provide an opening for a cheap shot, such as remerging Grindelwald from a horcrux. (Thematically, love shouldn't be a weakness, but Grindelwald may have forfeited that through his inhumanity to others.) We won't know until Ms Rowling decides to write on the topic...
...which will likely happen as part of the screenplays for the 5-movie Fantastic Beasts series. Apologies if it goes without saying to all y'all, but looking this up is the first that I knew that there will be not just one but four sequels to the Fantastic Beasts movie, all wrapped around the developing story of Dumbledore and Grindelwald.
Since it seems that the climax will be the great duel, I have to assume the way it will shake down is a show-stopping action sequence, mixed with heart-wrenching speeches and some twist, likely duplicitous. 'For the greater good'.
TL;DR: It's very likely we're going to see a huge wizard battle c. 2024 but there's going to have been some truth in Rita's words. What the truth is can be guessed at but the intervening four movies will likely rearrange a lot of the details.