You did the right thing.

The alternative would be to play blond and stupid. By the way I'm blond not stupid but I often feel that way. You could have said I saw that terrible cut on your arm, if you don't mind me asking what happened.

People often like to talk about themselves. People will sometimes talk to a stranger before a loved one because they know they will never see them again. I am the worlds worst for asking people things like that and finding they just needed someone to talk to. I have set for an hour or more w/ a stranger listened and prayed for them.

We live in a cold and unfriendly world. A kind word goes a long way. You did the right thing to. Sometimes it is odd to be approached by a stranger w/ questions.

I wouldn't worry about it to much. You did good.