It's more sophisticated than that. A single movie can be fragmented into 1000s of fragments, each fragment carries 1 bit. It's called A/B forensic watermarking. So you need to insert a 1-bit watermark into a video segment that is a few megabytes, there is no feasible way to defeat this as a pirate unless the watermarker is incompetent. Averaging will not work.

See AWS offering:

  For large-scale per-viewer, implement a content identification strategy that allows you to trace back to specific clients, such as per-user session-based watermarking. With this approach, media is conditioned during transcoding and the origin serves a uniquely identifiable pattern of media segments to the end user. A session to a user-mapping service receives encrypted user ID information in the header or cookies of the request context and uses this information to determine the uniquely identifiable pattern of media segments to serve to the viewer. This approach requires multiple distinctly watermarked copies of content to be transcoded, with a minimum of two sets of content for A/B watermarking. Forensic watermarking also requires YUV decompression, so encoding time for 4K feature length content can take upwards of 20 hours. DRM service providers in the AWS Partner Network (APN) are available to aid in the deployment of per-viewer content forensics.

<https://docs.aws.amazon.com/wellarchitected/latest/streaming...>

This will be more challenging for text. Not as difficult for images.

> the only place to do that is in the least significant bits

This is also false, it's the most naive way to watermark content. They do it in the mid range frequencies these days. And then make the watermarks robust to resizing, re-encoding, cropping and even rotation in some cases. They survive when someone holds a camera to record a screen.