Quite possible, actually.
All the posts I've read so far seem to talk about asymmetric encryption, or symmetric encryption. It is entirely possible to do what Bitcasa are claiming. Although I wonder if they got it right. Anyways, the classic Needham-Shcroeder protocol (assuming you replace nonces with timestamps) provides a good basis for it.
It works like this:
Alice is a subject that submits a file
Bob is a subject that has shared access to Alice's file
Sam is the Bitcasa server
Alice calls Sam and says she'd like to share a file with Bob.
Sam makes up a session key message consisting of Alice's name, Bob's name, a key for them to use, and a timestamp.
Sam encrypts all this under the key he shares with Alice, and he encrypts another copy of it under the key he shares with Bob.
He gives both ciphertexts to Alice.
Alice retrieves the key from the ciphertext that was encrypted for her, and passes on to Bob the ciphertext that was encrypted for him.
Next, Alice creates a hash of the unencrypted file, and sends that to Sam for indexing.
Alice now uploads her file to Sam, encrypted using the key from the ciphertext that was encrypted for her.
Bob has access anytime he likes, using the key from the ciphertext that was encrypted for him.
Simples. If, as I said, they got a). the protocol right and b). the implementation actually reflects the protocol.