So now that we suspect Abe Lincoln had Marfan’s disease because he exhibited what we now understand as manifestations of the disorder (although they seem unrelated), is there some condition that is associated with short, stubby thumbs and big toes? I’ve observed a person who almost lacks a final phalange on the thumb and toe. Or am I on to something completely new and irrelevant?
Fibrodysplasia Ossificans Progressiva
http://www.uphs.upenn.edu/ortho/fop/
Or the person you mentioned could just have short thumbs and toes.
I was born with very short, stubby thumbs. My final bone in my thumb is about 3/4". It is about half the size of a normal thumb tip. As a result, my thumbnail is approximately a 1/4" long. It looks like a spaceman visor. Other than that, I’m normal, and I have no deseases or ailments from it, and there are no other physical problems.
So, I have (like your friend) Stubby Thumb Syndrome. 
I’ll bump this, since I’m curious…I used to date a girl with one stubby thumb; she called it a “toe thumb,” and so got a lot of jokes after the Seinfeld episode about that (and, no, she didn’t have a toe transplanted to her hand – she was born with it).