I have seen rabbits acting this way in my area. Normally, they will run away very quickly. But they have been just sitting until I (and my dog!) are very near before they even notice us! My dog loves it! She will stand very still and stare at the rabbit until it finally moves, then she gives a half-hearted chase.There's plenty of (semi-)wild visitors where i live and on several occasions i witnessed an animal passing by very close to me totally disregarding my presence. It happens at night mostly. I had this situation with a fox, a hare and recently a weasel, all running no more than 2-3 meters from me standing on a pavement. Only after i had made a clear move they seemed to notice that i was there. Such tunnel vision isn't something that normally characterize wild animals. Maybe it's just adaptation to living in urbanized environment but to me it felt like they were in a mild trance of sorts.
Yesterday while sitting at my desk (I work from home), I kept hearing a mocking bird outside, really loud. I hear them often here and see them on my walks. When I looked out, it was sitting on the ground, just outside our fence, singing all kinds of tunes! I could see his little throat bulge with some of the sounds. Wow! What a wonderful little gift that helped my mood.