Also, api clients shouldn't give a damn about URI structure/content. If they aren't using links embedded within the representations you present then your "RESTful" API has bigger problems than the where-to-hide-the-version game.
Consider that a server may choose to provide the same resources in one of multiple versions and renderings, for instance to support older clients alongside new ones. I would consider it surprising if altering a resource at e.g. /v1/users/22 would also alter resources at other URLs, like /v2/users/22.
In addition, keeping version out of the URL allows the resources to be cross-referenced between different client apps, which are not necessarily browser-bound. One client expects the latest and greatest version, one client expects an older version, and they can pass data back and forth freely.
I agree, but I'm talking about returning e.g. /users/22 instead of /v1/users/22 or /v1/users/22.json, not instead of 22.