I'm mostly using common sense here, but let's see what would happen to a board when it's left with components in.
Oxidation would occur even with no components. Probably some parts of the springs would oxidate differently without components than if components are in, but contact surfaces would probably be more exposed without components in, so I don't think that having components in would make more bigger impact then just having board sit in same conditions without any components.
Next, let's take a look at problems which could come from components themselves. Most components don't produce any debris by just lying around, so only problem could be bad electrolytic capacitors which could leak and contaminate the board. Maybe broken LCD could contaminate board too? I can't think of any other components which leak at the time.
If we take a look at the contacts themselves, cold welding could cause problems if the components need to be removed and board repurposed for another use. I don't think that cold welding would cause problems with signal quality on the parts which were left there and allowed to weld, because that's what we use for standard network cables and it works. If the components are removed, contact surface of the springs could be damaged or contaminated by remains of the weld. How big problems this is would depend on materials used for springs and component leads.
I really don't know what happens to springs which are left in a certain non-relaxed position for extended periods of time, but there could be problems with that. But then again, I think that springs would wear out more by inserting and removing components.
In the end, I don't think there would be any reason for anything bad to happen if prototypes do remain assembled on a breadboard.
Since the myth comes from a school, maybe the biggest issue would be simple mechanical damage and problematic storage of breadboards. As far as I see it, components are exposed on top of a breadboard and can be damaged very easily. Also, it would be difficult to stack populated breadboards. On the other hand, I don't see anything breadboard specific here. Same rules would apply to any other type of prototyping board.