Pedantry dictates I must point out that everyone on that oath on a bike or walking has right of way at all times no matter who is around. What changes (or rather doesn't, because as is pointed out its negotiated space with no distinct rules on this) is 'priority'.
'Give away' signs do blur the distinction annoyingly, should really be 'Cede Priority'.
I'm interested in a defence of the cyclist overtaking the pedestrian being that she may have just misjudged the speed of the cyclist coming the other way. Undoubtedly that may be true, but just to throw it in there, if a car ahead was overtaking another car into the face of a cyclist and came within a whisker of a nasty crash (as here) would we accept the driver saying, "sorry, I misjudged your speed"?
As others have said, the sigh lines are pretty good and I just think a bit of looking ahead determines that the cyclists coming the other way 'may' get there before I do (as I say, that's usually my approach, which yes does sometimes mean I sometimes dawdle thinking, they're going slower than I thought, which is me misjudging the speed, but realising that's a possibility and so erring on the side of caution rather than taking a chance).
At the same time it is abundantly clear (especially with TFL's knowledge from sitting behind backpack boy) that he was an aggressive soul, and that sort of riding has no place on a shared use oath, and he also should have been looking ahead and noted that she was overtaking, and slowed rather than gone for an utterly barmy gap that wasn't there
That's really why I think there's fault on both side. Initially if she chooses not to overtake right there and then there's no incident; and if he, on noticing that she IS overtaking, slows down then there's no incident. Better actions by either sees nothing happen (and better actions by both is utopia).