Actually, there is another caveat here and potentially one that may eventually lead to no view counters on attachments (or at least for some types).
As of right now, video and audio attachments are served directly by the web server, rather than going through our PHP script. This is mostly for efficiency due to the way browsers make requests to these types of content. Thus, since the standard attachment viewing code is being bypassed, the view count won't be incremented. Overall, I think we'd consider that mostly as designed/expected for technical/efficiency reasons, with a likelihood that in the future, more attachment types (such as images) will be served in a similar way.