From the UX aspect, I actually would not expect it to be rejected. I would indeed expect to see something totally different than what I typed with a label nearby saying "Edited by $NAME 5 seconds ago"
I'd much rather see my edit form shown again, with my content still in it, and a conflict warning... Nothing worse than loosing that 20 minutes of typing to a conflict!
Wow, 20 minutes is a long time to spend on a "Github organisations description". But yes, I'm absolutely with you on that. Whenever I need to submit a long text field in an online form, I got into a habit of always first copying the contents into my clipboard, to prevent myself from causing irreperable harm to things around me if the request fails.
But going back to the UX, I would prefer that the site accepts my change and stores it in a journal (a-la git or Wikipedia), before overseeing it with the next change, so that I could easily revert to it or merge it with the newer change.
But this is easy to do. Just embed a version number (or hash) in the form. If after submitting the version to be changed is not the same as in the form, then you know there is a conflict.
I'd rather see the edit warning when multiple people are editing the same info before 20 minutes of typing even starts, and a interface for accessing history for the edge cases.