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 :-).
Cave deposits also often have distinctive structures of their own (e.g., spelothems like stalactites and stalagmites), so it is not likely that someone could mistake them for a successional sequence of rock units. Each of them is a testable hypothesis about the relationships between rock units and their characteristics.
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.
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).