I've just been talking with my AP about this over coffee.. It sounds as if things did not begin well between the two of you.
From what you've written the problems she's mentioned are to do with her perception of the welcome (how/where she arrived, and that she thought you'd be around during the day).
Is her English very good? If it's just intermediate or basic then maybe she can't express herself as she would like to. Maybe she doesn't mean she expected you to be at home all the time - but maybe she was expecting you to be there on her first full day with you - maybe you told her your previous AP would be there but she understood this incorrectly and thought you emant yourself.
With the airport arrival - it also sounds like this wasn't as she expected/wanted and not what you expected/wanted.
From what you have writen it would seem you hoped she would have fly into Heathrow or Gatwick (presumably because it's more convenient for you).
Heathrow I'm sure doesn't have low cost airlines flying here like Ryanair & Easyjet, so this option may have been out of the question especially if she was paying for her own flight as flying scheduled airlines like BA would be to oexpensive.
Not sure what other options she would have had have but I know the last few au pairs we've had have only got the option of flying into Luton airport with Wizz Air. So she possibly didn't choose to ignore you but had no other option.
Did you discuss travel arrangements in advance. If she came through an agency then they should have been involved in all of these logistics. My agency once went and collected someone in person when we couldn't pick them up ourselves.
Most families do meet the au pair at the airport. So if you put yourself into her shoes - she has arrived in a foreign country with all her luggage and then had to find out how to get the train to London. Luton is very local to me and I know it's a bit complicated because the train station isn't at the airport so she would have had to have found the right courtesy bus, then got to the train station, bought the right ticket, then found the right train.. Often you have to get a separate short train from Luton airport parkway to Luton town station.. so she may well have been very flustered or even annoyed you weren't there to meet her.
Another issue may be on the travel costs.. Did you buy her a ticker for the train in advance (like an e-ticket) or did she pay for it with her own money. Travel costs in the UK are expensive compared to most other countries so this may have taken away all of her spending money that she came with. This cost shoul dalso be covered by the family so is it possible that this is an outstanding issue for her but she is unscomfortable about asking for it back?
So if she's said you weren't very welcoming then maybe she is talking about this part and not referring to all the lovely things you'd got waiting in her bedroom for her.
I'm sorry if this looks as if I'm taking the au pair's side, but my own AP thinks these extra issues can really make a difference in those first few days - especially if someone is feeling nervous or confused.