I don't consider it inaccurate. Yes, you can recompile Lua to use a single other numerical type, typically integer, possibly even complex, because the source code uses a #define for this and has been carefully written to avoid mixing its number type with actual internal operations. That is considerate, but it does not give Lua a numerical stack but merely changes its single type, so you then forego the use of double.
And you need to recompile Lua for that, whereas you can just link with the standard libguile whatever your number requirements may be.
You can consider me a Lua fanboy, so if I mention a disadvantage in passing, it is rarely an advantage to dwell on it as I might have good reason for my opinion.