Williams made the point her slump is really only a stumble and maybe did not occasion parting with a caddy who had been with her for 10 of her 14 LPGA wins, including both majors.
Beyond saying "sometimes change can be a good thing", Ko has not explained her decision, though most feel it was prompted by finding the water at the US Open when going for the green - dropping from first to third, with speculation Hamilton either advocated the adventurous approach or failed to get his golfer's mental equilibrium right for such a clutch shot.
After all, it was Hamilton who talked Ko into a safety-first shot at the key moment at the ANA Inspiration earlier this year. Result: a birdie and her second major.
It all seemed oh-so-easy for Ko then. "To me, fun is the key," she said after winning the ANA. "I think fun is underrated. Obviously we need to be serious out there, and you need to try your best and you need to focus, but at the same time, you've got to have fun because we're out there for a long time ... I think when I have fun, that's when I play my best."
It's a fair bet Lydia isn't having as much fun right now. Firing a caddy is not just an employment matter. As the old golf commentator Henry Longhurst once said, a caddy is not just an assistant but "a guide, philosopher and friend".
Hamilton's been down this road before - he was fired by Yani Tseng, herself once at the peak of women's golf. The Taiwanese was world No 1 for over two years and was the youngest player, male or female, to win five majors. She ditched Hamilton during a downturn in form in 2012 and fired his replacement a few weeks later. More caddies down the track, her game has not returned. Still only 27, she is currently ranked 94th in the world.
It happens in golf; some fear it may be coming for Ko. There are concerns tinkering with her swing in an effort to find the comparatively short-hitting 19-year-old some more distance have not had the desired effect; she has developed a new tendency to miss left.
British golfer Luke Donald, a former world No 1, now 74th, also tried for more distance; his form deteriorated and has not returned. Even worse, he was fired by his caddy, John 'Long Socks' McLaren - a rare incidence of employee sacking boss; McLaren is currently with Briton Paul Casey, who plays in the US.
Ko is also no longer the new phenomenon; there are half-a-dozen challengers for her No 1 spot, including 18-year-old Canadian whizz-kid Brooke Henderson. Pressure.
Ko will come again. That famed temperament is her biggest weapon. Anyone who has watched her between shots knows her talk about "fun" isn't just talk.
She chats away to her caddy and playing companions and walks around with a grin on her face, for all the world like a teenage girl who has nothing more serious to do than update her Facebook page. It's a quality that should win many more tournaments - and majors.
It is also a rarity - a professional athlete who seems to like what she does. Andre Agassi is probably the best known athlete who didn't like his sport. Others who found their once enjoyable pastime had become a chore included Joe di Maggio, whose biography revealed he largely thought of baseball as a way to make money.
England cricket all-rounder Vic Marks once told an interviewer county cricketers spent much of their time searching the sky, hoping for rain.
Serena Williams said she preferred shopping or "sitting down" to tennis. British Premier League footballer Bobby Zamora said: "I'm not a massive football fan, really. Quite a lot more players than let on are the same. I don't watch games on an evening or anything like that."
The test for Ko will be when it stops being fun, now or later. If she, as the old saying goes, can keep her head while all round her are losing theirs - then she'll be a head taller than everyone else.
