I always have mixed feelings about these kinds of situations. On the one hand, I have a pretty routine life that doesn't push me to do new things, nor am I much interested in doing new things inherently. I don't drive so the majority of my transportation is either walking or friends giving me rides (which I plan in advance at mutual convenience, never demand, and always thank them for). I'm not very comfortable using public transportation, especially in a strange place (which I realize is not Mary's situation). So when I see the posts about how Mary should just "grow up" or how a 12-year-old should be able to ride the train alone just fine, I cringe a little, because it hits home with me.
But on the other hand, one of my pet peeves is people who don't accept the consequences of their decisions, and I try to do this myself. I could get around more on my own, via bus or cab, but I choose not to. If this means I miss out on doing things, or rather, I can only do them with other people in tow, then so be it. Or, if I really want something, I suck it up and figure out an alternate method. For example, I recently had to travel across the country for work. I needed to be at the airport at 5am--I would never ask a friend to get up and take me there, so I called a cab, even though that makes me more anxious than going with a friend would. I personally would just feel really pathetic asking a friend instead of confronting my anxiety and calling a cab. During some downtime on the trip I wanted to go to the zoo; the best way seemed to be, again, taking a cab, which again made me anxious. I told myself, either you take the cab, or you don't go to the zoo. So I took the cab, I went to the zoo, and I had a great time. (Much less anxiety taking the cab back from the zoo--I was so tired I would've crawled into a dump truck if it was going in the right direction!)
So I'm kind of torn about Mary. I've had the experience of confiding my anxiety about transportation to a friend, in the hopes they would have ideas I hadn't thought of or at least reassurance, and being told that I needed to grow up or get professional help or something like that, and it was very hurtful and made me feel like I shouldn't confide things to them. I would be grateful to a friend like the OP, who tried to help and reassure me, without changing her own plans in an unfair way. I would also understand if, in the future, a friend just didn't schedule something where I had to do something that made me anxious, as long as they didn't say that was the reason, even if it meant we didn't see each other as much.