No. Dropcam streams. There's no on-board storage. (Ok, maybe there's a megabyte or so - enough to store about one second of video for buffering before transmitting.)
How does that negate my statement? You don't have to store (much of) the video to process it locally on the device. As an example, it's being compressed before streaming. As to whether it does something with the video is another question, but it's definitely possible without storage.
... which is exactly what I said. You asked "It doesn't have to store the video to process it?", and I said no, it doesn't, other than a small amount for processing.