I think a closer analogy would be if your neighbor walked over while you weren't home and lifted on your garage door, noticed it wasn't locked, so went inside and poked around a little. Then came and warned you later that your garage door isn't locked and maybe you shouldn't store those bank statments in the garage.
What if he says that he has discovered that if he stands on one foot in the street in front of your house, holds anyone's garage door opener above his head, and clicks it 25 times at precisely 9:01am while shining a laser pointer at the top of the door, your garage door will open.
What matters is if the thing they're doing to test your security is similar to what criminals would do to breach your security.
In the case of a physical location, that bar is low. It's things like seeing if your garage door is open, or your car doors are locked, etc.
In the case of computer resources, that bar is high. Probing your database for permissions holes is absolutely something that a normal "cyber criminal" would do. It's the equivalent of a carjacker looking to see if your doors are unlocked.
So an "online neighbor" alerting you that your database is unprotected doesn't feel weird at all. It's not the equivalent of that weird laser pointer thing you talked about, it's the equivalent of looking to see if your car doors are unlocked while you're away on vacation.
Would I be upset at him? No. Would I want to have been told? Yes. Would I think he's a little weird? Yes. Would I want him to keep doing weird shit and letting me know if he finds any other similar issues? Yes.
Still missing something - the garage would have to be on your private property, not visible from public property, and the only way he could check for you is if he entered your property and tried to get into your garage.
On the contrary, I would say that this is a garage you rent on a public space. The internet is open and I can do requests to any server. If you don't want your system to answer me, make sure it does not.
If I am in front of an ATM on the public street, it doesn't give me money without authorization. Make sure your server does the same.
Streets are generally open. My house is on a public street - that doesn't entitle anyone to attempt to operate my garage door, let alone exploit a security vulnerability in its software to gain access. That's just trespassing.
The closer analogy would be your friendly neighbour warning you that he determined your garage door code was easily guessable after he spent 45 minutes entering different codes.