@guybrush
I sort of agree with what you have written, but it is possible to write this example without the loss of water. Since dichromate is technically an anhydride of chromic acid. The proton being removed concomitantly with the electrons being accepted by the chromium need not generate a water molecule (though that is commonly found in a mechanism).
There are two proton transfer reactions, one with the formation of a chromate ester (the CH3CH2OH) and the second to generate CH3CHO + H+. It is possible to remove one or both with a chromate oxygen and not water. I am not arguing that water must be avoided, only that it can be avoided. If it were avoided, then acetaldehyde is a more likely product because water can easily form a hydrate with acetaldehyde to form acetic acid.