Possibly because beliefs in invisible friends are not as unique as its various practitioners claim it is.
I'd beg to differ. In the case of the dharmic religions, while they do contain superstitious nonsense, they're not really predicated on the belief in a theistic god, or an 'invisible friend.'
Rather, they are more like mystical philosophies, which, like all philosophies, have at least some degree of truth in them.
What's particularly interesting about these philosophies is their inquiry into the human psyche, and a lot of what they have to say on said subject certainly has its validity. For example, the cause of dukkha/suffering being attachment, and in order to free oneself from suffering one must disenthrall oneself from one's desires and attachments.
I find myself agreeing with Sam Harris on this. That is, it is indeed possible to have a transcendent experience through meditation and following some of the practices of the eastern philosophies.
A lot of atheists reject the idea from the outset, as they associate it with religion and therefore believe that it's nonsense. Nevertheless, there's nothing that precludes a non-mystic or atheist from practicing meditation and benefitting from it.
I myself once had a rather strange experience with it, like a lucid dream. It's something that's happened a few times with me but I only fully pursued it once. The result was a rather strange and frightening thing that felt like an 'out of body' experience, although I don't believe that that's actually what happened.
In any case, it is something that begins with the feeling of oneself floating, but in motion, as if spinning or moving from side to side and its frequency gets faster and faster until it feels like a continuous, fluid thing. It feels like you're being pulled out of yourself, moving upwards as if coming out of the top of your head.
Eventually, it gets to the point where you feel like you have finally left your body, and all you can 'see' is blackness. Eventually, I saw an image of a room form in my mind. It formed in a very strange way, as if I was looking up, submerged under water and seeing the ripples on the surface of the water.
When the 'ripples' subsided, I could then see the image. It was like a messy room, with some object in the middle that stood out from other things, as it was an intense blue colour.
I was fully conscious during all of this, and I thought it was pretty freaky, so I woke myself up. It was strange when I did, as I noticed I was completely paralysed for about a few seconds. My eyes were open, and all I could do was see. But eventually, something just 'clicked' and I woke up fully, able to move.
Most likely what I saw really was nothing more than an image created by my mind, but I was fully conscious during all of it. At the same time, I remember having a kind of equanimity for a few days afterwards, a feeling of peace.
In any case, it makes me think that the human brain is capable of doing some rather interesting things and so I wouldn't be at all surprised if someone who spends years in meditation has some kind of transcendent experience.