Got it: apparently you need to tell the WebcamSubscriber to subscribe before setting the publisher.  You guys should have the class throw a relevant Error so users don't get confused.  Here's the code I used to find it:

package com.ironcoding.videochat {
   
    import com.adobe.rtc.authentication.AdobeHSAuthenticator;
    import com.adobe.rtc.collaboration.WebcamPublisher;
    import com.adobe.rtc.collaboration.WebcamSubscriber;
    import com.adobe.rtc.events.SessionEvent;
    import com.adobe.rtc.session.ConnectSession;
   
    import flash.display.Sprite;
   
    public class WebcamTest extends Sprite {
       
        protected const USERNAME:String = "";
        protected const PASSWORD:String = "";
        protected const ROOM_URL:String = "";
       
        protected var _cSession:ConnectSession;
       
        protected var _webcamPublisher:WebcamPublisher;
        protected var _localWebcamSubscriber:WebcamSubscriber;
       
        public function WebcamTest() {
            var authenticator = new AdobeHSAuthenticator();
            authenticator.userName = this.USERNAME;
            authenticator.password = this.PASSWORD;
           
            this._cSession = new ConnectSession();
            this._cSession.addEventListener(SessionEvent.SYNCHRONIZATION_CHANGE, this.onLogin);
           
            this._cSession.roomURL = this.ROOM_URL;
            this._cSession.authenticator = authenticator;
            this._cSession.login();
        }
       
        public function onLogin(event:SessionEvent):void {
           
            this._webcamPublisher = new WebcamPublisher();
            this._localWebcamSubscriber = new WebcamSubscriber();
           
            this._webcamPublisher.publish();

            //Without this line, it crashes.  With it, it doesn't.
            //this._localWebcamSubscriber.subscribe();
            this._localWebcamSubscriber.webcamPublisher = this._webcamPublisher;
        }
    }
}