What specific part of what I said was incorrect?
Pretty much all of it! You've presumably gone to wikipedia and looked up "Binaural Recording" and then incorrectly applied that definition to "Binaural" in general. Then, because you think that binaural only refers to binaural recording, you've simply made up the statement that a sound designer cannot create a "binaural effect" unless a binaural recording technique has been employed. And, even your definition of "binaural recording" is only partially correct! Why present "facts" which you know you've just made up? Furthermore, why do this when you know there is someone already involved in the thread who does know about audio? The only logical conclusion is that you're deliberately trying to mislead the OP, cause a dispute and/or derail the thread, the very definition of an internet Troll!
OP: It's maybe useful, as a filmmaker, to know in general terms what binaural is but you don't need to have a detailed understanding of it, the way I explained it previously is probably sufficient. However, to put the record straight, here is a slightly more detailed explanation: When listening to something on headphones we hear two ISOLATED audio channels (Left and Right), however when we listen to speakers (or to sound in real life), we don't. The audio output by the right speaker in a stereo system is not only heard by the right ear but also by the left ear, which is not the case when using headphones. In the case of say a sound which is panned to the right speaker, the sound waves hit your right ear AND travel through your head to your left ear. The sound hitting your left ear is different though, it is delayed, it arrives at your left ear a fraction of a second later than it arrives at your right ear. Additionally, it has a different level and frequency content, as your head absorbs some of the sound, a little like the difference between hearing a sound and hearing the same sound through a closed door. These timing, frequency and level differences are collectively called Head Related Transfer Functions (HRTFs). This may all sound like irrelevant scientific mumbo-jumbo but it turns out that our brains rely on these (sometimes tiny) differences to compute/create our perception of sound, even though we're not consciously aware of that computational process. In a similar way that we're not usually consciously aware that our brain is computing two separate (and slightly different) visual images into a single visual perception of the world we see. A binaural mix is one which tries to overcome the problem of the isolated audio inputs to each ear (in the case of headphones) by applying artificial/simulated HRTFs. There are 3 different (and exclusive) ways to do this: 1. To use a dummy head and two mics placed where the ears would be, to actually record a sound signal which includes simulated HRTFs (this method is not suited to the vast majority of filmmaking though), or 2. To use binaural panning tools during the mixing process, which add mathematically modelled HRTFs or 3. Processors are available which will take a completed (non-binaural) stereophonic mix and apply HRTFs to generate a binaural mix.
While all this might be mildly interesting (or thoroughly boring!), as I said, it's not really relevant to your current situation unless you plan on providing two different versions of your film and/or instructing your audience to only listen with headphones.
G