All encryption methods have a secret key that needs to be stored somewhere. The quote doesn't say that he can't "disclose the method to access it", it only says that there is no password involved. That's a much weaker statement.
This question basically comes down to whether there are encryption schemes that do not rely on a human brain for storing the secret. The answer is Yes. These two come to mind off the top of my head:
- Public-key encryption: As suggested in comments, if he sent the data to a friend, encrypted with their public key and then deleted his copy, then Edward Snowden would legitimately no longer have access to the data (but the friend can give it back to him if needed).
- Hardware based encryption: by this I mean any system where the encryption key is stored in hardware. An example would be a laptop with full disk encryption where the keys are stored on a smart card; unless you have the card, no amount of password-telling with decrypt the harddrive!
- Low Tech It's also possible that he's using a lower-tech solution than you are imagining, for example generating a random 64 character password, writing it down on paper and giving the paper to a friend or storing it in a bank vault.
I'm not trying to imply that any of these are convenient, or even particularly good security measures, but they count as "passwordless encryption" enough to make his statement true. Or maybe he does have some magical encryption system whereby he, and only he, has access to the data regardless of how much information he gives you.
About journalists: I have helped a few journalists set up digital encryption systems, and I completely agree with that quote that technical ability and attitude towards protecting sensitive information varies wildly from journalist to journalist!