Re: when Thatcher said
Yes, I now see that it is unverified.
In my defence I can only say that I have in the past had considerable doubts about people who claimed that Thatcher never made some crass remark. That's because I have been repeatedly assured that she never said "there is no such thing as society..." whereas I actually had a recording of the speech where she said it.
Regardless of whether she made the public transport remark, a lot of Conservatives, in my experience, are rather anti any public transport that doesn't get them to and from central London. It's that prejudice that I was mentioning.