Just found this thread and very glad as my DD (2.6) is just the same - no probs with wees in potty or loo, but happier to go without a poo for days than to do one except in a nappy. She also refuses to do a poo at her CM, or with DP - yes, lucky mummy is the only one whose company can be tolerated at poo time.
I am happy with giving her a nappy for it rather than deal with the mess because I think if this is about her self control, then encouraging her to ask for a nappy is a good stepping stone that works for both of us (she gets seriously distressed when she does a poo in her knickers).
Anyway, what I really want to say is a bit of armchair psychology as a friend who helps look after her, had a real insight when she realised that DD was actually feeling scared of answering the question 'have you done a poo?' after she had done one in her knickers, as either 'yes' or 'no' made her feel ashamed (yes = I've made a mess, no = I'm lying), ie a lose-lose situation.
So what we're doing is this
a) trying to welcome poos in the nappy. I know this sounds insane but I now say 'hello big brown poo' or start a discussion about whether it's a small, medium or big poo. She's definitely most proud of big ones. This is to help get over any anxiety she might have about producing it, and being uncertain whether it's OK.
b) encouraging her to ask for a nappy if she wants a poo and praising her for doing so, because this is her controlling what happens and therefore good as an interim step. I'm assuming she'll eventually want to do poos in a potty or loo at a later stage, and meanwhile poos in nappies are easily managed.
c) not talking about presents (even though this worked like a dream with wees), because I have a hunch that she feels it adds pressure somehow. She definitely already knows that what's expected of her, she's just not ready to do it yet.
d) I am going to try poo in pooland and see how it goes.
So, that's my pennyworth (no pun intended)!