This is.... Absurdly cute. What the fuck.
It's worth noting that the reason the beaver wants the water to be deeper in the first place is that the Beaver is using the deep water as a pantry:
All summer and fall, beavers gather up branches with the leaves they actually eat, and store it in the deep end of the Pond, where the cold water and limited oxygen keep the leaves fresh all winter, so when it's negative 20 outside, a beaver can take a dip out of it's lodge, grab some refrigerated leaves in the (relatively) warmer water and go back to it's cozy little nap hole while everything else is out there suffering and eating bark or the like.
So it's less "there's a leak in my house" and more "OH SHIT THE FRIDGE!!"
This instinct is so deep-rooted that if you play an AUDIO RECORDING of running water around beavers, they will immediately show up with mud and sticks trying to patch the nonexistent leak.
So in short, yes, when they see/hear running water and think "absolutely not"
imaginig beavers yelling "THE FRIDGE!" like my mum yells "THE LAUNDRY!" when it starts raining
