Woods crashed out of the £1.7million HSBC-sponsored championship on Thursday night, just like world number one Rory McIlroy, after he was given a two-stroke penalty for getting the rules wrong after consulting playing partner Kaymer.
Instead of surviving by one shot the 14-major champion bowed out by one - the first time in his 16-year professional career he has not been around for the weekend in a non-PGA Tour event.
Kaymer, though, resumed in joint seventh place only four places behind his Ryder Cup teammate.
Three times the winner of the title, the German did not realise what was about to unfold when Woods called him over to inspect his lie after hitting his drive into ice-plants on the fifth hole of his second round.
"He said 'Is it embedded?' and then I walked away - we both thought it was a (free) drop," Kaymer stated.
"But then obviously the referee came up to us on 11 and said the sand area was not like normal grass, so he was apparently not allowed to drop it.
"I didn't know about it and he obviously didn't know about it, otherwise he wouldn't have done it. It's an unfortunate thing."
Before departing for his long flight home - he competes in San Diego this coming week - Woods said of European Tour senior referee Andy McFee's decision: "Andy feels the way he feels about it, then I broke the rules."
McFee explained: "When we got into the recording area (after Woods had just missed a birdie putt on the last) I asked if he wanted to go out and have a look.
"He said 'Look, if you think that's the right ruling that's good enough for me'."
All this was long after Rose had added a 69 to his opening 67 for an eight under par total that left him one ahead of Welshman Jamie Donaldson, Dane Thorbjorn Olesen and Spaniard Gonzalo Fernandez-Castano.