While entirely true that The Great Escape was not a documentary, it was based on a non-fiction book of the same name by Paul Brickhill, who was in fact involved as a POW in the very real Great Escape, though due to claustrophobia he did not participate in the actual tunneling or the escape itself.
The characters in the film were based on real men and composites of real men. The character "Cooler King" Virgil Hilts, played by Steve McQueen, whom we see sent to solitary multiple times, was based on David M. Jones, who participated in the Doolittle Raid, survived same and escaped captivity at that time, only to be shot down in North Africa and sent to the very real Stalag Luft III. He actually led the digging team on the real tunnel "Harry".
On balance I believe The Great Escape is about the closest thing to an accurate depiction of such an arresting historic episode as you can get in a dramatic film.