No, Steno's principle of original horizontality (I'll call it the POOH) is not 'safe'. It is not a useful theory.
Don't confuse it with the law of superposition (also due to Steno), which is useful. That law is, in a general sense, a foundation stone (ha!) of stratigraphy... with some caveats due to resedimentation and other processes.
Why is the POOH dodgy? On small and large scales, the concept of 'layer-cake' stratigraphy does not hold up. Indeed, it's probably rather unhelpful. Brian Romans wrote a nice essay on this subject in 52 Things... Geology (edited by me, 2014) — see the link below. In it, he refers to Bailey (1998), who described sedimentary bodies as 'lenticles' with complex 3D geometries. And you just have to look at some seismic reflection data from the continental shelf to appreciate that this principle applies to even an outwardly rather continuous environment (excerpt of a line in the Virtual Seismic Atlas):
Bailey, R (1998). Review: Stratigraphy, Meta-Stratigraphy, and Chaos. Terra Nova 10, 222-230. DOI: 10.1046/j.1365- 3121.1998.00192.x
Romans, B (2014). Strata are not flat. In: M Hall, ed., 52 Things You Should Know About Geology. Agile Libre, Nova Scotia, 132 pp. ISBN 978-0-9879594-2-3. Available online.