Yes, and yes
The answer to your first question (I've re-worded it a bit)...
is the outside world, such as the image of other people, a reconstruction of the collection of sensory inputs that are processed and merged in the brain?
...is simply and straightforwardly a 'yes'. Sensations picked up in the periphery are collected and processed centrally in the brain. So yes, it is all in the eye of the beholder, and as Bach-y-Rita (2003) famously put it:
We see with the brain, not the eyes
Your second question is a more interesting one in my opinion, namely
...are perceptions of the outside world all processed in the brain and then projected, as if they were outside?
The answer here is also 'yes', quite obviously given the answer to the first question, yet it is a fascinating and active interdisciplinary area of research spanning psychology, neuroscience and philosophy. It is of much interest now, given the COVID-19 crisis, and the many hours people spend talking to computer screens instead of 'real' colleagues, friends or family.
The phenomenon you are referring to is beknown to me as distal attribution (Auvrey et al.,2005), which can be defined as:
...the ability to attribute the cause of our proximal sensory stimulation to an exterior and distinct object
The phenomenon has attracted a lot of interest in the arena of sensory substitution, where a lost sense (e.g. vision) is replaced by another (e.g. touch) (Stronks et al., 2015). An example device is the BrainPort V100, where visual information is transferred from a head-worn camera to a tactile display worn on the tongue (Stronks et al.., 2016) (Fig. 1). The cool thing in regard to your question is that blind folks using this or similar devices have been reported to feel a disconnection between outside and the tactile information the device provides on their tongue. However, after prolonged use, subjects using a related (predecessor) device of the BrainPort, the TVSS, reported that they started to feel the tactile sensations to be actually located outside of their body. Specifically, this happened when the users were able to direct the camera image themselves, rather than receiving static images projected onto their backs.
The TVSS system is shown in Fig. 2. It was a massive device built in the 1960's by Bach-y-Rita and colleagues to substitute vision for tactile sensations. The camera is on the left in the picture and the 200-tactor display is mounted in the rest of the back support of the dental chair. At first the camera was held stationary to project stationary images onto the back of the subjects. While successful, the tactile images on the back lacked the feeling of externalization. However, when the users were able to handle the camera themselves, they started to actually sense the objects to be 'out there' in space.I note, however, that these observations are rather anecdotal, but were obtained from reputable sources. The experiments are dealt with in White (1970).
Fig. 1. BrainPortV100 device. It consists of an electrotactile tongue display unit connected to a glasses-worn camera. picture courtesy: News Salute
Fig. 2. Bach-y-Rita's Tactile to Vision Substitution System (TVSS). picture courtesy: Tongue Vision
- Auvrey et al., J Integr Neurosci; 4 (4), 505-21
- Bach-y-Rita et al, Int J Human-Computer Interact (2003): 15(2): 285-95]
- Stronks et al., Brain Res (2015); 1624: 140-52
- Stronks et al., Exp Rev Med Dev (2016);13(10): 919-31
- White, IEEE Trans Man–Machine Syst (1970); 11:54–58