It is not only a documentation error.
In Matlab, the default behavior is to extrapolate for values outside the range. Here is the Matlab result:

>> X=[0,0.5,1];Y=X;Z=X;
>> V=rand(3,3,3);
>> x=[-0.1,0,0.1]; y=x;z=x;
>> interp3(X,Y,Z,V,x,y,z,'spline')

ans =
    0.2796    0.8147    0.8973

In Octave the last command would result in a NA for the first answer.

The interp3 function searches for values in a pre-defined list. It has an option to extrapolate the values outside of this list (this is actually the default Matlab behaviour). However, when this option is used, an error is given.

Example:

>> X=[0,0.5,1]; Y=X; Z=X;
>> V=rand(3,3,3);
>> x=[-0.1,0,0.1]; y=x; z=x;
>> interp3(X,Y,Z,V,x,y,z,"spline")

ans =

        NA
   0.26611
   0.26838

(In this case, the default Octave behaviour is to return an "NA" for every outlier. However, I would like to extrapolate the values via the "extrap" option).

>> interp3(X,Y,Z,V,x,y,z,"spline","extrap")

error: interp3: wrong number or incorrectly formatted input arguments
error: called from:
error:   C:\Octave\Octave-3.8.2\share\octave\3.8.2\m\general\interp3.m a
t line 134, column 5

>>

Octave does not accept the "extrap" option in the interp3 function.