The monk in that video that this bearded man is criticizing was clearly giving very simplified teachings for the general public. His explanations and his manner of speaking did appear kind of lame, at least when taken out of context. I can see how he was easy for this man to criticize.
The monk did not speak very well about science. I sometimes think that the integration of Buddhism and science has been negative in some ways. When Buddhists talk about science which they don't know much about, they are not serving the interests of Buddhism or science. Also, all the hype about the parallels between Buddhism and science has created the exaggerated expectations in the public that they have now discovered the "truly scientific religion." People can get very bitter when they discover that Buddhism requires assumptions which can be neither proved nor disproved by science.
This video lecture was not the best that Buddhism has to offer. The monk in the video was like a wounded deer for this skeptic to pounce on. The bearded man should watch a Buddhist master like the Dalai Lama give more sophisticated teachings on karma and rebirth.
Ian Stevenson's work is probably some of the most compelling modern evidence for rebirth, but I can understand how many skeptics say that many other explanations are possible. Clearly more work needs to be done in this field; however, much of this research wil involve interviewing children, and a skeptic always has the ready answer of "Well, they're just kids. They have no idea what they're really talking about. They're just making things up." The desire not to believe can be as strong as the desire to believe, and skepticism can be its own religion. What is needed is an unbiased researcher, and if one reads more about Dr. Stevenson, one will find that he was very objective and did not set out with the intention to prove rebirth. And it should be noted that there is other evidence for rebirth besides Stevenson's work. But in the end, one has to simply read the ancient Buddhist masters and decide for oneself whether these masters were talking sense or not.
The bearded man said that it is arrogance to make statements about what a person doesn't know about. However, the nature of consciousness remains the greatest mystery of modern science and scientists still know very little about its exact nature. So, this man should refrain from talking about what he doesn't know about. How does he know that Buddhist masters have not experienced their past lives during meditation? Can he prove that they did not? Much about the mind is still unkown to science. Heck, even qualia is still a hard problem in cognitive science.
I do not know much about the critic in this video, but I get the suspicion that he secretly admires some parts of Buddhism (sort of like when 6th grades boys tease girls they secretly have a crush on). He seems to enjoy the metaphorical interpretation of rebirth. Although I would not call that traditional Buddhism, if he loves some parts of Buddhism, I encourage him to keep on loving them. Maybe his brief exposure to Buddhism in this life might lead to him actually becoming a Buddhist in his next life.