There's a middle ground between "My lawn needs watering" and "My family died today in a terrible car crash". And you are assuming he HAS some intense need for connection, like the dude is contemplating suicide and ONLY THIS CONVERSATION CAN STOP HIM FROM JUMPING OFF A BRIDGE. "YOU MUST ACT UPSET ABOUT MY LAWN OR I WILL KILL MYSELF!" If this guy's that desperate for sympathy, he definitely needs to go to friends or family or even a psychiatrist, not some-dude-on-the-street. I don't know who's going around telling lawn stories to do some weird transference of totally empty, token sympathy to some major issue in their life.
Beyond that, I think he choose a stupid topic for conversation, essentially. Talk about a shared experience between you and the other person, such as work or school or whatever. Talk about something from pop culture one is likely to know about and be able to talk about. If you are starting a conversation, you could first ask the other person about themselves, like everyone with any sense does. Talk about something else that's at least theoretically interesting. I don't start conversations with people I don't know well by saying "My computer's outta memory! I gotta clear up some space later! Probably I'll delete these things which you have no conception about, because you have never seen nor probably will ever see my computer, and even if you did it still wouldn't matter in the slightest" because I seriously doubt that would go anywhere as a topic. It's a topic the other person has no knowledge of, and has no way to contribute to in any meaningful way. It's almost rude. If I talk to a stranger, I try and use relatable topics they have knowledge or probable knowledge of, and can contribute to. I expect others to have a similar courtesy.
Would I actually have told someone off for sharing such a pointless thing? No. It would probably actually go:
Person: [Insert exceedingly banal problem]
Me: Oh, that sucks.
Me, in my head: Why are you telling me this? Why do you think I want to discuss this thing, which is entirely boring and unrelated to me, with you, essentially a stranger?
Unless he very quickly changed the topic to something I could actually talk about, that's it. End of conversation. If he tried to press on with the same topic, I'd probably claim that I had to go or was in a hurry or something. No one has gained anything. The entire exchange was utterly pointless and a waste of time.
I'll talk to strangers, but if all they're talking about is how cute it is when their kitty Snookums, a cat I do not know nor will ever know, sneezes, then I am going to leave as quickly as possible because I am going to consider it a waste of time.