If you don't have access to Timo's reference there is also the free resource
J.Stix On cuspidal sections of algebraic fundamental groups http://arxiv.org/abs/0809.0017 Appendix B
Beware that this appendix was suppressed from the published version (eponymous article on Jakob's webpage).
And yes, the argument is due to Grothendieck. You can find the original letter here :
http://www.math.jussieu.fr/~leila/grothendieckcircle/GtoF.pdf