案: why is a bench also a case? Sorry about the cryptic title.
案 is a character that can mean &quot;bench&quot;/&quot;desk&quot; but it can also mean &quot;(legal) case&quot; or &quot;file&quot;:


长形的桌子或架起来代替桌子用的长木板：～子。～板。书～。条～。拍～而起。

提出计划、方法和建议的文件或记录：档～。备～。议～。提～。方～。有～可查。～卷。～牍。



How does this one character come to mean two very different things? The radicals suggest that the original definition may have only been the &quot;bench&quot; one, and the second definition is only incidentally related - I guess people would look at legal cases on a bench or table, but it seems a bit of a stretch.
Your understanding seems to be correct. For example, in Liu Yuxi of Tang Dynasty's 《陋室铭》:


  无丝竹之乱耳，无案牍之劳形


Where 案 means the desk, and 牍 is a type of hard wood board or pad, on which you write articles. Put together, the bisyllabic word simply means cases, articles, or documents.