however, no chord can ever actually be an A7 without an A in it.
I suppose one could say this, but it seems awfully semantic.
I mean, first of all, what would you call (low to high) G-C#-E if you don't call it A7?
I guess you could call it Em6/G if you wanted, but that's not a common voicing for Em6, and it is a very common voicing for A7.
Secondly, music theory is really nothing more than applying names and terms for musical devices and explanations for how and why things work. It allows us to communicate with other musicians, but it
doesn't exist in a vaccum. The "rules" of music theory are broken
all the time, and if it's been communicated by two musicians that this is an A7 chord, then why can't it be?
Thirdly, if a guitarist is playing a solo arrangement and plays this chord, and it sounds (in context) like an A7, and he's thinking of it as an A7, and the audience is hearing it as an A7 ... and ... etc.
A rose by any other name ....
Walks like a duck, talks like a duck ....
etc.