I remember it vividly. The story was about a doctor running up to another doctor, in front of Feynman's wife and her family, and was excited to the point of being rude, asking things like "Did you check for X?!" where X was a symptom of tuberculosis that Feynman had also noticed. The doctor was admonished for his behavior and for "making the patient feel uncomfortable" and was brushed off, even though he was on the right track and would have diagnosed the tuberculosis sooner. Feynman could have stepped in and said "Well, actually, I also noticed X," but the social pressures of the situation persuaded him to stay quiet, which turned out to be regrettable.

It probably isn't in Wikipedia because it isn't in Surely You're Joking, which is freely available online, whereas you have to buy the other book which has this story. But the story is definitely in there.

EDIT: Here's the story: http://pastebin.com/NeP4Ka70

Some summary:

...

As soon as I hear about [the disease] I go down to the library at Princeton and look up lymphatic diseases, and find “Swelling of the Lymphatic Glands. (1) Tuberculosis of the lymphatic glands. This is very easy to diagnose…”—so I figure this isn’t what Arlene has, because the doctors are having trouble trying to figure it out.

...

The county hospital gave Arlene all sorts of tests and X-ray treatments for this “Hodgkin’s disease—?” and there were special meetings to discuss this peculiar case. I remember waiting for her outside, in the hall. When the meeting was over, the nurse wheeled her out in a wheelchair. All of a sudden a little guy comes running out of the meeting room and catches up with us. “Tell me,” he says, out of breath, “do you spit up blood? Have you ever coughed up blood?”
The nurse says, “Go away! Go away! What kind of thing is that to ask of a patient!”—and brushes him away. Then she turned to us and said, “That man is a doctor from the neighborhood who comes to the meetings and is always making trouble. That’s not the kind of thing to ask of a patient!”
I didn’t catch on. The doctor was checking a certain possibility, and if I had been smart, I would have asked him what it was.

...

[A long time passes, and Arlene's condition worsens. The doctors finally perform a biopsy to figure out what's wrong.]

...

When I got to Arlene's house, she showed me the report. It said, “Biopsy shows tuberculosis of the lymphatic gland.”
That really got me. I mean, that was the first goddamn thing on the list! I passed it by, because the book said it was easy to diagnose, and because the doctors were having so much trouble trying to figure out what it was. I assumed they had checked the obvious case. And it was the obvious case: the man who had come running out of the meeting room asking “Do you spit up blood?” had the right idea. He knew what it probably was!

I felt like a jerk, because I had passed over the obvious possibility by using circumstantial evidence—which isn’t any good—and by assuming the doctors were more intelligent than they were. Otherwise, I would have suggested it right off, and perhaps the doctor would have diagnosed Arlene’s disease way back then as “tuberculosis of the lymphatic gland—?” I was a dope. I’ve learned, since then.