Question: I was just reading an e-book and saw this sentence which really confused me:

[![enter image description here](https://i.stack.imgur.com/CuYCV.png)](https://i.stack.imgur.com/CuYCV.png)

"Played twice as fast as written" - This isn't what cut time actually means right, or are there situations where cut time means exactly that?

I thought cut time is basically just 2/2 time signature, but the speed would still depend on the bpm and the note durations...

Answer: 
That sentence "Played twice as fast as written" indicates that someone must have a misunderstanding. Someone who probably thinks that quarter notes are supposed to be played at a certain speed. That person would need more knowledge and experience with both tempo markings and different kinds of time signatures.

I suppose you could say that in the beginning when you learn your first note values and make your first exercises with the values you do get used to think of quarter notes as indicating some basic speed. You need to crawl before you can walk so to speak. But you certainly better learn to walk before you write a work book on the matter.
No, it's not current... and it doesn't really make much sense. (How fast is it "written"?)

Your assertion that time signatures do not dictate tempo is correct. Certain meters might imply faster tempi (6/4 is probably going to be used for slower pieces, and 12/16 is usually seen in fast pieces like gigues) but those are general usages, not requirements.