Yes, the lady giving out credit card details should be more careful. But she would have to be unlucky for someone to hear her conversation and take advantage. Airports are probably a common place for this to happen though so a good place for a thief to be.
In the case of the company conversation. If you placed the notes you had taken in this blog and identified them then someone who wanted to do them harm could search and find that information. Once it is digitised it is much more dangerous.
I've been thinking about this and considering conversations in private or public about health:
http://wishfulthinkinginmedicaleducation.blogspot.com/2010/08/my-thoughts-on-health-professionals-and.html

I always wonder this myself. Usually it's the too much information phone calls: medical problems, or swearing at the other caller. Then I wonder if I give up too much information on the phone. (There was a fun Radio Shack / Lance Armstrong commercial along the lines of why people yell into their mobile phones.)

In short: people operate under the mistaken belief that the phone call is private in a public setting.

It's as if some people have never took to heart the saying 'discretion is the better part of valour'. Saying 'I will call you later' or stepping aside to take a call is almost non-existant. The worst I've faced was on a train, sitting next to a sufferer of verbal diarrhoea who was letting loose in the shrillest of north-Chinese accented Mandarin about some double-crossing friend and her piccadilloes. After half a minute I drew her a look and proceeded to tell her in no uncertain terms to pipe down. Worked a charm.

Perhaps there is an underlying inferiority complex in that they feel they are unworthy of the attention of the people around them, or that the information they are giving away to the world is just not worth the trouble...a health dose of paranoia is always useful in information security.

I work for a large company that requires all employees to go through an annual course reminding us to protect information when we're out in public. It's the sort of repetition that leads one to complain that it's unnecessary and "Certainly everyone knows not to talk about this sort of thing in public, right?"

Your experience would tend to indicate that continued repetition of the message is probably a necessary thing.

I have thought exactly the same thing at airports when I had to phone regarding unlocking my card which had been locked from usage abroad, that the very tools credit card companies use to stop theft (tell us the three digits on the back of the card) become useless if somebody overhears us repeating it to someone.
I hid in a corner looking very furtive, then completed my call.