Fullwidth solutionorgrid with exam-class

Question

The exam-class provides a convenient environment for typesetting either a specified kind of space for students to solve the question or the solution to that question, based on given class options. My problem is, that using the solutionorgrid is always indented with the question, so there is a lot of space wasted.

I looked at the definition of solutionorgrid and \fillwithgrid[<length>], which solutionorgrid seems to be using, but i couldn't figure out how the width of the typset environment is determined.

There is a \fullwidth{} command, but it doesn't work for solutionorgrid or even only \fillwithgrid[<length>].

Also there are questions around here, that answer similar issues, but none of them really solves my problem.

MWE:

\documentclass[a4paper, 12pt]{exam}
% \documentclass[a4paper, 12pt, answers]{exam}

\usepackage{showframe}

\begin{document}
\begin{questions}

\question
  Why ist there air?

  % \fullwidth{ % <== works as expected
  %   \begin{solution}
  %     Because we couldn't breath without air.
  %   \end{solution}
  % }

  % \fullwidth{\fillwithgrid[\stretch{1}]} % <== throws error

  \fullwidth{ % <== works for solutions but doesn't print grid
  \begin{solutionorgrid}[\stretch{1}]
    Because we couldn't breath without air.
  \end{solutionorgrid}
  }

\end{questions}
\end{document}