When debug output is enabled, any calls to ezdebug executed in the context of the rest API trigger a call to php trigger_error.

This in turn will send the error to the screen, breaking rest output.

It is particularly annoying because it can happen after the code implementing the rest call and the filter chain, where the end user can put an ob_start() or an error_reporting( 0 ) call.
A prime example of this is the ezformtoken extension