The only way I can do this, is to argue it from the point of claims that space is a vacuum.
If it's not...then we are being lied to.
If it is...we are being lied to.
So either way, we're being lied to.
To clarify, space is not a perfect vacuum. A perfect vacuum is a volume of space that contains absolutely no matter, not even a single sub-atomic particle. Space does contain matter, but in miniscule quantities, meaning that it is not a perfect vacuum, but it's close enough for general discussions on the subject.
On another point, do you understand that "psi" is an acronym for "pounds per square inch"? You seem to be confusing it with volume, which would be in cubic inches, cubic feet, gallons, litres, etc.
The larger the chamber...the stronger it has to be, because it has an enormous amount of psi inside it and an enormous amount surrounding the outside of it, equalizing it from inside and out.
This doesn't make a lot of sense. If the chamber is at 0psi inside, and the atmosphere is at 14.7psi outside, then the pressures are clearly not equalised (0 ≠ 14.7). If what you were trying to say was that there is a lot of nothing inside, and a lot of air outside, that would be more correct.
Simply put, a pressure vessel of any kind does not equalise with the surrounding environment, it actually
maintains a difference in pressure between the inside and outside of the vessel. That is the purpose of a pressure vessel. If it did what you suggest, it would be useless, as it would not retain any pressure.