Yes. Motion Lab analyzes your video inside your browser, so the video file is not uploaded during analysis, and SwingVantage does not share it publicly. It stays on your device.
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Your browser also keeps the 6 most recent clips on the device, so you can re-analyze one without uploading it again. Those copies do not leave the device either.
When you are signed in, a saved analysis can include one still frame used to draw your swing trace, and it syncs with the analysis; deleting the analysis removes it. Beyond that, two optional features can send part of a clip — a limited set of still frames, never the full video — and both only run if you choose them: a cloud re-read offered when your device could not read the footage, and an "AI second opinion" you can start from the One Fix step of your results. See what leaves your device.