That doesn't seem like it could be true. The film is rolling through the camera, and if the shutter were open continuously, the entire film would be a vertical blur of light. The shutter would open and close once per frame, so the film can be advanced. The actual shutter speed of a camera shooting 24 fps would be much faster than 1/24 s.
You're right about the continuous roll. Film actually moves through the gate incrementally. There's a really neat mechanism that closes the shutter and advances the film to the next frame in one elegant move. But while the film is exposed, it's exposed for a fraction of a second. Meaning that any motion occurring within that second will register with a blur in that particular frame.
It is really interesting how our brain compensates for the motion blur in films. I mean, you don't usually notice that things are really blurry until you pause the movie.
Our brain compensates for motion blur, period, because everything we see is effectively slightly blurred due to our eyes' response to light changes being non-instantaneous.
Specifically, cone response time seems to be on the order of 15-20ms if I read http://www.ncbi.nlm.nih.gov/pubmed/14990682 correctly. And that's just to go from initial stimulation to peak response; presumably the response also dies off in nonzero time, so the full width of the response in time is more than 20ms. Rods respond slower than cones according to http://en.wikipedia.org/wiki/Photoreceptor_cell though I can't find numbers.
