Maybe I'm missing something but aren't most women in labour meant to get themselves to hospital? Obviously in this case it would have been better if she had had one - but people regularly have fast labours resulting in babies being born in taxis, in cars, or at home because they didn't get to hospital in time. Just because she was walking doesn't make a huge difference.... and she could have got a taxi - if it was that close it would hardly have cost much.
Plus when I was in labour I was told to go for a walk!
Yes she's annoyed but this sounds like a case of hospital made a decision, it turned out to be wrong in this case but seems to have been fairly reasonable. And they said they would investigate any complaint so fair enough. What are they supposed to say?