Can BetterDisplay record the signals traveling over an HDMI cable?

No. BetterDisplay does not capture or analyze the live traffic traveling through the HDMI cable. Its display information, reports and app logs are not a raw HDMI trace.

You can inspect the reported display and connection configuration, and use supported DDC or HDMI-CEC features to send commands. Those capabilities do not turn the Mac into an analyzer for everything exchanged between the Mac, an adapter or receiver, and the display.

A normal-looking screen recording shows the captured image, but does not prove that the HDMI output and the receiving display are behaving correctly. When investigating a black screen or color problem, compare the direct connection and available output modes. See Display Information and HDMI-CEC diagnostics.