I would call this the "Schrodinger's Byzantine Friendship Problem".

You start with a case where the Yes or No are equally probable. Then you apply functions to this system that may or may not change the outcome to the "Yes" state. And then you make the measurement.

No matter how many times you have applied that function there's always a probability the person in question is lying, or otherwise - there's always a possibility a person is simply afraid of opening up and is hiding behind politeness.

Point being - you can't analyse it too much. You can't make progress in science without experimenting. Neither can you progress in relationships. Sometimes it backfires. Sometimes it may even backfire more often than not. But it still is working with experimental data.

There's no binary relationship status that suddenly switches people from "casual chat" to "going out for beers". What makes inviting someone out for a beer expected and normal is that your relationship is one where you often invite them out for beer. That means if you've never done it before, it's probably going to be a little bit awkward regardless. (Unless there's a culture of inviting random new people for beer, which is not uncommon.)

But unless you're absolute strangers, I don't think many people are going to think "weirdo", they'll just be slightly surprised.

Still, "awkward when you call them up for a beer" is hardly the stuff of nightmares -- or enough to label anyone "socially incompetent weirdo".

You don't need to be best buddies with someone to call them for a beer.

In fact calling a new acquaintance for a beer is how many friendships actually get build.