Dear Sotiacho,
I have had an opportunity to discuss the matter with a colleague and think about it as well. While the following answer stares at us in the face, I accept that it is simplistic, perhaps wrong and it also raises more questions.
If dichromate is going to reduce then it would be in proximity to a reducing agent. However, for the reduction to be successful the electron transfer would have to occur (@ 3e-s per chromium atom) and the ion would have to break up fto result free chromium III ions. (presumably due to a newfound instability). This break-up would be facilitated and occur only if there are a heap of free protons(hydrogen ions) in solution whereby the "freed" oxide ions could bond with two protons to form water. Otherwise there would be free oxide ions in solution and that just doesn't happen in aqueous solution to any appreciable extent;
Clumsy, simplistic and perhaps incorrect - but I find it logical for the moment.
The main question that is raised is: Does dichromate become unstable when it manages to accept 6 electrons? I guess so, but does the instability only cause the break up to be complete when there are hydrogen ions present to facilitate the boding to oxides as they're released?
See you tomorrow.