> As far as the Lua C API is concerned, stack values are function arguments.
In the C standard, the definition of 'argument' is certainly not dependent on Lua's stack values.
In the standard C library API, an effort is made to warn the user of undefined behavior when an argument is valid at the basic C level, but semantically it is not. For example, fopen(): "The argument mode points to a string. If the string is one of the following, the file is open in the indicated mode. Otherwise, the behavior is undefined."
Compare that with the current note for lua_tointegerx(): "The Lua value must be an integer, or a number or string convertible to an integer (see §3.4.3); otherwise, lua_tointegerx returns 0", and then compare with an imaginary note for lua_next(): "The value at the given index must be a table; otherwise, the behavior is undefined".