I'm hoping they are frugal and have parties with non-family members at their homes. Maybe a barbecue where neighbours invite their friends... and they invite friends of friends...

As someone who lives in Indiana, this is probably it. Big gatherings usually end up with a few people that the host doesn't know (of course, that's true most places).

The "at home" location is the location of the person when they submitted the missed connection form. For example, my location is "at home" as I type this.

No, it says it's the "location where the missed connection occurred."

Deliveries, solicitors, repair people, friends of neighbors, passers-by out for a walk/jog/ride, etc.

I read it initially as symbolic - feeling estranged in a relationship, so it feels even at home like ships passing in the night. But, I think the other explanations here are more likely :)

Yeah I was confused by this too.

People in Indiana, do you have a lot of strangers over for parties or something?

Perhaps a roommate that is in love with the other?