Reading the article on the response from Twitter, it might not have been entirely helpful in the second response with the use of the 'pet' or 'love' question, but aside from that it doesn't sound like Virgin did much wrong. The customer says that the train guard said 'you go ahead, honey' in an aggressive tone, but unless someone can confirm that completely I will take it with a pinch of salt and assume she may have interpreted it that way. For all we know the guard could've even said it in a way of encouragement or even in a way where he didn't agree with it but won't stop her from doing so.
The only person we are actually hearing about this from is the customer themselves though, and given the fact this person felt the need to refer to the guard as an 'old male' and immediately jump to the conclusion that it was a form of sexism and belittlement, and given that she is pictured holding a cup of coffee, along with her dress code and use of certain words, I honestly wouldn't be surprised if she was one of those fragile middle-class moral busybodies who can't handle a word like 'honey' because of her own personal association with the word. But for now I shall not pass confident judgement, because I don't know this person.
You could argue that Virgin responded poorly to her complaining about it and need to apologise for that, but they do not need to apologise for the "offence caused", because this woman being offended is HER choice, not some forced decision by Virgin and their old sexist male guards. If we can hear the other side of the story and maybe some other accounts of the situation, we can come to a better conclusion, but instead we already have a few people claiming sexism and patronising attitudes towards women. Unless you were there and know what happened, or have heard both sides of the story, it's a one-sided judgement.
I don't like the word 'babe', and I don't particularly enjoy being called it, but I won't stop someone of customer service using it for example because, to them, it may have a different meaning and it may be their way of being friendly. Therefore, I won't really bat much of an eyelid because I don't try and police what people say just because I don't like the word used, instead I just let them say it when it's something as harmless as 'babe' or 'honey' etc. I would only get annoyed if I asked them to stop and they chose to ignore it, but that's it. The point I'm making is we've only heard one side of the story and need the other sides, though I worry we won't get it.