It is not an assumption, it is a fact.
It is necessary to clarify what it means for an object to “exist out there”. To do so, I will break the phrase up in individual words: exist, out and there.
What does it mean for something to “exist”? It means that it has the potential to be perceived. Something exists insofar it can be perceived. It need not be perceived in order to exist, but it must have the potential to be perceived.
Example: a bottle of wine sitting on a table exists regardless of whether there is anyone in the room perceiving it or not. It does so because if anyone wanted to perceive it he could do so by entering the room and then looking at the bottle with his own eyes.
What does it mean for something to exist “there”? It means that it can only be perceived by using specific approach.
Example: a bottle of wine sitting on a table can only be perceived by placing oneself in the correct position: inside the room where the bottle is and by looking in the direction of the location od bottle.
What does it mean for something to exist “out” there? It means that it can be perceived using an approach that is not included in the given set of approaches. “In” and “out” are words that tell us whether an element is included within a given set or not.
Example: if our set of positions contains every position on Mars, then our bottle of wine, which is somewhere on Earth, is not included in it, and therefore, it exists out there and not in there.
In our case, the given set is what is termed “subject”. What does it contain? Every brain in the universe, right?
In such a case, an object that “exists out there” would be an object that can be perceived but not by perceiving brains.
How does one perceive a brain?
There are two ways: using your external senses, by looking at someone’s physical configuration of the brain, or using your internal senses, by tuning into your own body (e.g. recalling a memory, focusing on a bodily feeling, etc.)
None of these approaches would work.
Now, when you say that no object exists out there, what you’re saying is that no object can be perceived using a specific set of approaches. These are any approaches that are not included in the given set.
Again, this set is identified by the word “subject”. This is why I asked you to define the word: so that we can know which approaches can help us perceive reality.
Given my definition of the term “subject”, your claim would mean that no object can be perceived without perceiving a brain, which is demonstrably false.
A bottle of wine sitting on my table is not, and cannot be, perceived by perceiving my own brain, using my internal senses, or someone else’s brain, using my external senses.
It is a fact that objects “exist there” and it is a fact that some objects “exist out there”.