the clip and explanation are only to provide a practical basis for responding to questions regarding the options available to a referee who has applied advantage to a foul which interferes with a goal or an obvious goalscoring opportunity.
Some general principles need to be recalled:
Given a foul judged to be an interference with a goal or a goalscoring opportunity and given the referee's decision to apply advantage, the following scenarios should be considered carefully:
In the Chivas-Revolution clip, New England's Taylor Twellman (No. 20) was fouled by Carlos Llamosa (No. 11) at the 39th minute. The referee applied advantage (though this is not evident from the clip). Several seconds later, the referee judged that the advantage had been lost (the foul slowed Twellman sufficiently that an opponent was able to catch up to and challenge him). The referee stopped play for the original foul and, prior to the restart, cautioned Llamosa. If the original foul had been considered an interference with an obvious goalscoring opportunity, the correct referee action would have been to send off Llamosa for "denied goal by foul" (DGF).
In the Arsenal-Barcelona match, the referee stopped play after the Arsenal goalkeeper, Jens Lehmann, fouled Barcelona's Samuel Eto'o at the 18th minute at the top of the Arsenal penalty area. Just after the whistle was blown, Barcelona teammate Ludovic Giuly came streaking in from the right and struck the ball into the net. The goal was canceled and Lehmann was sent off. If the referee had allowed the advantage to develop, the offended team would have scored and, prior to the kick-off, Lehmann should have been cautioned. The goal, regrettably, was not valid because the referee decided the advantage had not continued and stopped play before the ball was struck into the net. Under these circumstances, the referee had no choice but to return to the original decision that a goalscoring opportunity had been denied -- Lehmann was sent off and shown the red card.