Sounds terrible in that clip, but the sound gets so distorted when recording using a mobile, it's not really that useful, sadly. That said, it sounds a bit like a loose spark plug.
As for the loose pulley scenario, I'm surprised Mr Autolusso hasn't seen this before, being an established specialist. The cambelt drive pulley starts to move and wear into the locating key before the oil pump drive becomes loose enough to spin and cause the low oil warning to illuminate. I've seen this at least half a dozen times now, and only on one occasion was there an indication of low oil pressure. I think I have some of the damaged bits from the last one rattling about in the bottom of my tool box; I'll see if I can take some pictures which should help explain what happens.