There is enough information, you're just looking into it too much. She's just asking if calling someone "old man" is ok, instead of using their name, "Hey, old man". It's not the same when you attached their real name to it or simply state the fact that they're an old man like in your 2nd example.
@Jennifer15: "Sir" or "mister" would be polite, if you didn't know the man's name. "Old man" as a term of address isn't rude because it mentions age, but because it isn't respectful.
I, for one, am frankly aware of exactly how long I've been alive, by the way. Having it pointed out in conversation by anyone but my doctors is generally unnecessary.
That said, "old" is less dismissive than terms like "elderly" or "senior citizen."