When not recognized as one's own, projected thoughts are perceived as 'other'. Not me; not mine.
They then "seem" as if they belong to environment.*; they are then perceived as such. (project:- to cast out).
Perceptions can be mirage/illusion/misperception. If we don't recognize a thought as our own, then the only other place, where we can perceive it, must be in the environment; there's no other place they could be. Therefore, we react to unrecognized thoughts as perceptions.
What's "apparent/obvious", can still be illusion/mirage. (Like the 'flat earth' of yore; that perception is still with us.)
* Echos are projected sound;- we recognize as such.
Images projected are-NOT as easily recognized as our own; (unless we investigate or are told. (When children hear a echo for the FIRST time, they are usually 'fooled', so they are told how it 'works'.)
(See #81 in the thread; "Sometimes we don't distinguish thoughts from perceptions:" it's a 'companion' to the above.)