You’re missing the point. To have a valid argument your assumption or assertion must be backed by some kind of coherent and relevant reasoning to have a valid conclusion.
Indeed, assumptions need to have a basis, ie, based on something objective and unchanging.
But I was actually referring to the “coherent reasoning” aspect when I said something to the effect of “following the same process”.
Two people can be the most rational and intelligent and logical people around, and both following flawless logic, reach different conclusions because they started from different assumptions.