That's one of the attachment types referenced in the original article. "I am uncomfortable being without close relationships, but I sometimes worry that others don't value me as much as I value them."
Attachment theory has a sound experimental basis, and is the dominant model used in the study of child behaviour. Its use with adults is less dominant, but is still very much mainstream psychological practice.
Being unable to tell the difference between someone that likes you versus someone who is just being polite, and if you consider them a "friend" and act "accordingly" they would consider you a socially incompetent weirdo.
About 90% of the time, it is not a big deal. I do try to make sure we are on the same page about some things. Most of the time, it is only an issue if some guy imagines it is a budding romance because he almost never talks to anyone, so talking to me occasionally is a big deal to him and he is imagining this is heading to bed when it isn't remotely on track for that in my mind.
I have had genuine friendships and other close relationships with introverts. I know how that plays out and that can work. Problems arise when people get weird ideas like because they talk to me once in a while, they have some special claim on me and I am not supposed to have other friends.
Keep in mind that it takes two to tango, even platonically, and if you like dancing with this person but they like dancing a lot more than you do, it is not reasonable to expect them to sit on the sidelines waiting for you. Let them dance with other people in peace at times when you don't want to dance anyway. It isn't taking anything away from you if they are consistent about being available for you when you need a friend.
Interesting that you would say that. After a few painful and confusing months I finally decided to reduce contact with a female ex-flatmate of mine to a minimum. The conclusion I arrived at, is that she's pretty much exactly the type of person you described here. I simply can't handle that. It's confusing and I never know where I stand with her and that just adds too much unnecessary pressure in an area of my life where I just want to feel well (interpersonal relations / friendships). So, for my own well-being, I can't have her in my life anymore.
Just wanted to share that, since your comment summarized my impression of her so perfectly!
I've felt the same concern and still do from time to time. The truth is relationships are a mixed bag and people are all different. Some people really will think you're a socially incompetent weirdo. Other people will wonder if you're thinking that about them. And some people will just find you to be a likeable person.
Ultimately if/when some other people don't like you, well, that doesn't define who you are as a person or that you need to be fixed. It's just not the right fit between you, and that's nobody's fault. It's going to happen, and it only matters as much as you decide it matters. It really doesn't need to matter!
Be yourself, focus less on your perceived shortcomings/insecurities, and focus more on improving other people's day.
I think the idea is that you consider that friendly conversation as a start of a friendship whereas the other person doesn't, so it might be awkward when you call them up for a beer or something.
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.
As an introvert, I used to get fooled by this in college, I would think that this person was somewhat close when they in fact had 100 other friends in my position... After a while though, you understand that their level of empathy just doesn't measure up to your expectations and you gradually part ways.
It's a mental model thing. Speaking freely (and probably self-disclosing along the way) is usually a sign of getting/being close. They see that behavior and think if they exhibited it, that's what it would mean. Which I think is a great example of how there are different "types" whether it be personality types, attachment types, what have you. Once you recognize there are types and that to a first approximation there are a finite, manageable amount of different types, you can learn how they differ and not get trapped by mistaking your mental model for everyone else's mental model. It seems obvious yet people seem to repeatedly make this same mistake as demonstrated by OPs experience.
As one more random data point: I am a chatty extravert. Sometimes people imagine they are close to me when they are not.