I’ve heard people say such things, but it is a thoroughly confused way of talking. Reality is “what exists”, nobody seriously claims that reality does not exist. There is another notion of “same reality”, the “multiverse” view that has become more popular recently where there are copies of the universe “out there” that we can’t see except if we are superheroes. Supposing that this is sorta true, that discovery would just tell us of a new aspect of existence that we did not know of before, some “phase” property where we ordinarily only interact with existents that are “in phase” with us. “We” live in this phase-universe, “they” live in another phase universe, all that Objectivism has to say about that is what all scientists have to say about that, namely “Where is your evidence?”.
Instead, what they mean when they talk of “same reality” is that it is impossible to directly know anything, instead every consciousness creates its own internal state specific to that consciousness, and there is no causal relationship between reality and that internal (subjective) mental state. Now, it is true that mental states are individual, that there is no such thing as a collective consciousness where you and I literally share the contents of a single mind. What the subjectivists seem to believe, which we reject, is that knowledge is uncaused. Nobody has come up with a coherent description of this “subjective reality” idea, so the best way to understand it is to understand what Objectivism says about existence and knowledge, then investigate what it would even mean to deny that position.
Objectivism says that we have anatomical devices which sense certain things about reality, such as sound, heat, color, and so on. We use these devices to perceive the universe. We cannot directly perceive x-rays or sounds above 60 KHz, and we even know these facts (and why they are true). We also have cognitive devices that allow us to retain and organize this sensory input. These devices operate in a physically-regular fashion, just as electromagnetic radiation operates in a physically-regular fashion. Humans are special no Earth in that we have some unique cognitive devices for retaining sensory information. In particular, we organize sensory information into general “concepts” based on common properties. We can reduce (primary) colors to frequencies, the wavelength of the light emitted, where “red” is about 430 THz and “blue” is about 750 THz. You simply have to learn the conventional boundaries for your culture, something that you do as a child (where there may not be a difference between “green” and “yellow”, just as English doesn’t have the Russian distinction sinij vs goluboj). The decision to organize sensory inputs one way vs. another is voluntary, in the sense that it is not immutably predetermined by the universe. Because we choose how to organize our knowledge, some people get the confused impression that this means that knowledge is random, chaotic and uncaused.
The concept of “proof” presupposes the Objectivist viewpoint. If you insist that knowledge is subjective and random, then the notion of “proof” or “true” is meaningless.