If I'm supposed to play a line cliche, usually I see it like this: E /D# | /C# /B |
So yeah, if you have that kind of thing in context, the intention becomes obvious. But apart from a line cliche, and having a E/C# chord outside of that context, it is an E triad over C# triad. That being a fact, I won't argue that point any further.
It is not a fact. I routinely see the "slash chord" designation used in charts where it is clearly intended to designate a non-chord tone bass note, rather than a polychord. I'm currently playing a production of Hairspray, for example, where the following progression is extremely common:
C | Am | F | F/G
The F/G in this instance is clearly intended to desigate an F triad over a G bass rather than an F triad over a G triad.