I don't doubt that this is possible. This particular video looks a little odd in that they immediately placed the monk into the coffin and closed it. I think that normally they would wait, check body temperature and heartbeat. I heard one story where a lay meditator went into samadhi and his wife could not wake him. The emergency medical team pronounced him dead and then he woke up on a table at the morgue.
One monk at the Las Vegas monastery recently died. I heard second hand information from a lay friend that his body remained warm for several hours after he was pronounced dead. This was taken to be a good sign that he passed away to a good destination since the body did not turn cold quickly. It was assumed that his mind was focused at the time of death.
As for Buddhist monks leaving the body at the time of their choosing, or maybe just seeing ahead when Yama is coming, I think it is definitely achievable. Genuine Theravada Buddhist monks keep all the precepts from the time of the Buddha with very little modification for modern developments. They speak little, sleep little, and eat little. They cultivate the Brahma viharas of loving kindness, sharing in other's good fortune, compassion, and equanimity. The daily fast at the temple I go to is from noon until 6 a.m. the following day. The monks are required to study the Suttas, memorize prayers and pass comprehensive examinations. They meditate. They observe celibacy. They have the protection of robes and precepts. And in return they have received generous support of lay followers for the past 2600 years.
It's all about practice and development of insights, samadhi and jhanas BEFORE the time of death. Practice and restraint! And of course this depends on the vipaka (results of previous actions) that follows one for the near and distance past from this and previous lives.
The annapanasatti practice can definitely lead to this achievement.