This orientation is not an assumption, because in virtually all situations, it is also possible to determine the original "way up" in the stratigraphic succession from "way up indicators".
For example, wave ripples have their pointed crests on the "up" side, and more rounded troughs on the "down" side.
Many other indicators are commonly present, including ones that can even tell you the angle of the depositional surface at the time ("geopetal structures"), "assuming" that gravity was "down" at the time, which isn't much of an assumption :-).
In more complicated situations, like in a mountain belt, there are often faults, folds, and other structural complications that have deformed and "chopped up" the original stratigraphy.
Geochronologists do not claim that radiometric dating is foolproof (no scientific method is), but it does work reliably for most samples.
It is these highly consistent and reliable samples, rather than the tricky ones, that have to be falsified for "young Earth" theories to have any scientific plausibility, not to mention the need to falsify huge amounts of evidence from other techniques.
They are the "initial working hypotheses" to be tested further by data.
Using these principles, it is possible to construct an interpretation of the sequence of events for any geological situation, even on other planets (e.g., a crater impact can cut into an older, pre-existing surface, or craters may overlap, revealing their relative ages).
The most common rocks observed in this form are sedimentary rocks (derived from what were formerly sediments), and extrusive igneous rocks (e.g., lavas, volcanic ash, and other formerly molten rocks extruded onto the Earth's surface).
They are applied by geologists in the same sense that a "null hypothesis" is in statistics -- not necessarily correct, just testable.
In the last 200 or more years of their application, they are valid, but geologists do not assume they are.
An early summary of them is found in Charles Lyell's .
In no way are they meant to imply there are no exceptions.
Despite this, the "principle of cross cutting relationships" can be used to determine the sequence of deposition, folds, and faults based on their intersections -- if folds and faults deform or cut across the sedimentary layers and surfaces, then they obviously came after deposition of the sediments.