The outer weatherstripping is secondary, not the primary seal. I believe it's there more to keep out road noise than anything, otherwise I'm not sure why the gasket material is there, it doesn't seem to serve any other purpose. I always clean the area above the lower weatherstripping when I wash the CR-V as it always collects road grime, this is the same for everyone. It's the first Honda vehicle I've owned that has any weatherstripping that far down on the door. So, it's not really "leaking" as it's not a complete seal in the first place. If you are getting water inside the cabin, then I would agree that you have a problem.
For the OP that is having the gasket tear, I agree with the previous post that applying some silicone to the gasket will most likely fix the problem if the gasket is getting frozen and stuck to the other surface. Honda recommends Shin-Etsu silicone grease. A tube of that will last you for years. It's something that everyone should apply every few years to their vehicles to prevent the seals and weatherstripping from aging.
