Comes across as genuine when someone is showing signs of struggling, and that's out of character or unusual.

I don't think it's cold hearted. More like it's normal. If every sob story was met with the attraction and help from gullible minds, you'd see a never ending stream of "new accounts" in turmoil surrounded by the help of strangers. That's simply not how life works though.

I think it's wise to always consider every possible outcome including the thought someone might be taking you for a ride. For your own safety as well. Old lady could flag you down, tell you she needs help moving a chair, so you enter her home, and three days later you're still tied up in the basement while some crazy guy prances around wearing only socks.