For error(), Matlab documentation is explicit that the input is a scalar struct.  It just happens to look a lot like what you would get if you did "struct (MException)".

Exceptions are objects (not structures) in Matlab. `throw` is a method of the MException class.
ISTR, that at some point in the past, we didn't want to implement getReport as a function because it also is a method of the MException class in Matlab. Should the same apply here?

Octave has the function rethrow(EXCEPTION) which throws an exception using the provided EXCEPTION structure.  When rethrowing an exception, Octave uses the stack field from the structure which points to where the exception originated.  Matlab has an additional function throw(EXCEPTION) which throws an exception, but the stack field contains the location where the throw() command was executed.  An example:

try
  error ("emitting an error");   # line 2
catch EXCEPTION
  rethrow (EXCEPTION);           # line 4
  #throw (EXCEPTION);             # line 5
end

Output in Octave is

error: emitting an error
error: called from
    tst_throw at line 2 column 3

If rethrow() is commented out and throw() existed then the output would be

error: emitting an error
error: called from
    tst_throw at line 5 column 3

This seems like a relatively easy function to add since, for example, the error() function already has the code to figure out where it is being called from in an m-file.