Ajahn Brahm has his own particular style of teaching that requires some getting used to . And while in my opinion all of his teachings are firmly based in the word of the Buddha as found in the EBTs, sometimes these teachings are adapted for making other (though equally valid) points to be carried across. (And don’t be fooled by this, Ajahn Brahm can just as easily quote in Pali with direct reference to the sutta when appropriate for the particular audience as he can “free form” it when it makes a greater impact to deliver a point wrapped in a story).
This particular story (the two monks in samadhi/sloth and torpor) is usually told at meditation retreats and serves as a reminder that “striving” is not to be done in meditation, because the main point of meditation is letting go.
As an example of Ajahn Brahm’s skill in storytelling you will perhaps be familiar with the “Anger eating demon” story, which is adapted from SN 11.22 (and you can decide which version makes a greater impact on you ):
Near Sāvatthī in Jeta’s Grove. “Once upon a time, mendicants, there was a native spirit who was ugly and deformed. He sat on the throne of Sakka, lord of gods. But the gods of the Thirty-Three complained, grumbled, and objected: ‘It’s incredible, it’s amazing! This ugly and deformed spirit is sitting on the throne of Sakka, the lord of gods.’ But the more the gods complained, the more attractive, good-looking, and lovely that spirit became.
So the gods went up to Sakka and told him what had happened, adding: ‘Surely, good sir, that must be the anger-eating spirit!’
Then Sakka went up to that spirit, arranged his robe over one shoulder, knelt with his right knee on the ground, raised his joined palms toward the anger-eating spirit, and pronounced his name three times: ‘Good sir, I am Sakka, lord of gods! Good sir, I am Sakka, the lord of gods!’ But the more Sakka pronounced his name, the uglier and more deformed the spirit became. Until eventually it vanished right there. Then Sakka, lord of gods, guiding the gods of the Thirty-Three, recited this verse:
‘My mind isn’t easily upset;
I’m not easily drawn into the maelstrom.
I don’t get angry for long,
anger doesn’t last in me.
When I do get angry I don’t speak harshly,
nor do I advertise my own virtues.
I carefully restrain myself
out of regard for my own welfare.’”