The main reason this has attracted so much attention is because the initial story wasn't adding up.
On the 28th December (shortly after she was last seen on Christmas Day), The Palace had announced a variety of Spring engagements for the Princess, including a
planned tour of Italy and more focus on her
"Shaping Us" campaign for the Centre for Early Childhood Royal Foundation.
Allegedly later that same day a police convoy and ambulance rushed out of Sandringham (where Kate and the rest of the Royals were spending Christmas) all the way to Marylebone in London (there were some photos etc. on twitter) where the London Clinic is (the London Clinic is the largest private hospital in the UK and often treats royals)
The Palace didn't say anything but announced in mid-January that Kate had gone in for a "planned abdominal surgery" at the London Clinic. Close friends apparently were "blindsided" by this according to Palace sources (while this sounds like gossip, the Royal Family correspondents have a complex web of reporting and sources). This resulted in planned appointments being cancelled (through to Trooping The Colour in June), but if it had been planned then it's not clear why the appointments were made in the first place. Shortly after there's a hatchet job on Kate published by The Mirror painting her as a crazy bitch, which
is then hastily edited to be about Prince Harry. There's archives showing the original (and look at the URL) but
the Internet Archive is now throwing errors.
A Spanish journalist, Concha Calleja, went on national TV in Spain around this time claiming to have a very trusted inside source (and it's worth noting their expert nanny/bodyguard who works closely with Kate, Maria Teresa Turrion Borrallo, is Spanish) and insisting that the Palace was lying and that actually Kate had been in hospital since the 28th of December.
During her hospital stay, William was seen visiting only once and the children weren't seen visiting at all. She was discharged shortly after Charles also began treatment at the London Clinic and "returned home" (and by comparison there were multiple noted visits to the King - this radio silence is very at odds with Royal PR). That Spanish journalist then reiterated not only that the Palace was lying, but that Kate had been in a medically induced coma and her life was in "great danger", and "an entire hospital" had been set up at the Princess's home.
Will remains evasive after this point, claiming he's "focusing on work" and possibly appears
drunk at the investiture ceremony, swaying and blinking weirdly and dropping a medal. He also issues a statement on Gaza using only his crest (the W)

rather than the normal Kensington Palace header they use to show unity

Suddenly, at the end of February, Wills short notice pulls out of a reading at his
Godfather's memorial service and a few days later Kate is seemingly spotted for the first time since Christmas in a drive with her mother.
Subsequently there's the weird family shot photo that
seems to have digitally altered outfits matching an excursion by the Royal family back in November (it's too autistic for me to get into on this already autistic post). The very first time we actually hear from Kate directly (supposedly) is after that photo gets pulled by the press and Kate goes "oopsie I photoshopped it haha". And then we get another pap shot which may in fact be a digitally altered photo from Christmas -

- and the accompanying explanation is confused (seemingly Kate rode with William in a car to a Royal Engagement she did not attend).
So it's PR-fumble after PR-fumble if the official story is true and it has left loads of gaps where this speculation has arisen - not so much "did Kate photoshop the pictures" but "did the Palace photoshop a picture to make it look like Kate is ok".
I think the clearest point is that the surgery in January cannot have been planned much in advance, as they wouldn't have announced the Spring plans only to cancel them. Possibly she's had a medical emergency and they're trying to downplay it, or there were serious complications that resulted (or maybe she's just got post-surgery moonface and doesn't want to be seen). But also there's arguments to be had that Kate was either completely AWOL or was in some way refusing to cooperate with the Royal PR machine (due to the marriage being on the rocks?). Feasible (but unlikely) is she demanded some plastic surgery ahead of short-notice becoming Queen if Charles is really taking a turn for the worse, she had to get psychological treatment for bulimia ahead of being Queen, she bulimia'd herself into needing hospital treatment or indeed that Wills is a wife beater and the palace weren't sure if Kate would recover. My personal favourite is she drunkenly cut her own bangs and is trying to grow them out without people noticing.