But direct wards already have this: if you go for the "free Intelligo" interpretation, then direct wards also have an innate knowledge of what a body is (ie, it knows that a beaver is a beaver.) As such, it's not a stretch to include that it can also have a free intelligo effect on what caused the object to move.
However - I also don't care for the free Intelligo effect. Hence my "blindly push against the innate property of an object" idea. It's similar to how you can use DEO as a "free Intelligo" effect to detect the infernal: if it starts smoking and screaming, then it's a demon. Or in this case: if the water parts, then you know the flood was caused by a beaver.
From my understanding of DEO - it blindly attacks the innate nature of the object, regardless of what an Intelligo would say about the target. Which means that Hermetic magic can affect something without actually knowing what it is. (ie, it can simply try, and if it fails then literally no harm done.) Therefore, it's not unreasonable to have an indirect ward that says "if you were put in motion by a beaver, then you can't cross" - regardless of whether or not the spell knows if the target was put in motion by a beaver.
Or to think of it another way: a Rego ward effect is a command to cease any Beaver-related movement in whatever attempts to cross its boarder. If there isn't any beaver-related movement? Then nothing is cancelled out. The spell doesn't need to know if there were any beavers in the command chain or not, just like a Perdo Vim spell doesn't need to know if the target is actually a demon. if there isn't - nothing happens. If there is, then something does.
EDIT - so in that sense, you can think of a ward as simply being a command, which then hands a chunk of magical energy to the object that allows it to reposition itself. So it's not the ward knowing that the flood was caused by a beaver. Rather, it's the ward telling the water "if you were caused by a beaver, use this magical energy to revert to a still state." The water then does the check itself, and if necessary uses the energy supplied.
Similarly, a magi could use a ReMe effect to command a target to "fall asleep", without first checking to see if the target actually has the ability to sleep: If the target doesn't have the ability to fall asleep, it simply doesn't work. We don't consider this to be an Intelligo effect, even though the failure state does supply information. Similarly, we can conceive of warding effects as a command to "stop all beaver-related activities", and if nothing happens, then we learn that there wasn't a beaver directly involved....or that there was a magic beaver, and we didn't penetrate his MR.