According to the Prologue of Henry II by W. L Warren, citing William of Malmesbury, Henry of Huntingdon, Eadmer, and Orderic Vitalis,

The last to embark were the younger members of the royal entourage, including the sons of the barons ... There was no more than a gentle breeze and a calm sea ... the drunken helmsman ...put the ship's head hard upon a rock in the bay [Barfleur harbor]. ... Some abandoned ship and rowed away in the dinghy, but put back to pick up one of the king's young illegitimate daughters, and so many other people tried to clamber aboard that it too sank. Only one man, clinging all night to the mast of the wreck, survived to tell the tale.

Google Maps says that the modern Barfleur harbor had no points more than 200 m from shore, but of course some shores have changed a lot. A calm night, 200 m from shore, and no sailors managed to swim it? This, and some answers in previous threads in this subreddit (though none with a definitive source), makes me think that few could swim and dive. This Web page author writes "very few of them would know how to swim" and states that the captain was in the water and chose to drown from despair.

But on the other hand, your source has more details (partly Orderic, it seems):

it would have been a very dark night (the moon was less than a quarter full on that date). People on the shore and even in Henry’s own boat could hear the sounds of people screaming, but they did not where it was coming from.

Phases of the Moon: 1101 to 1200 says it was 3 days past new, so it set shortly after sunset ... but I gather starlight can be helpful without artificial light.

Anyway. Aside from ability to swim, I expect that sons of lords may not have had a lot of wealth. Also, I don't know how much portable wealth they would have been carrying -- consider the loaded connotations of the phrase "real property" and that it means land. Other large sources of wealth: Horses (loaded on a ship to cross the Channel in the winter? shudder)? Armor? Also, I expect anyone with jewelry may have been wearing it, so it either came ashore or was lost somewhere in the water.

Sorry not to have a good solid answer, but I hope the citations and quotations will induce the moderators to have mercy on this reply.

(BTW, I think his mass-murder theory is ridiculous.)

(As a tangent, a few sources I found: Physical and Chemical Oceanography, and Physical Resources, by F. T. Banner says that surface temperatures in November nowadays are around 13 C. Hypothermia Table suggests 1-2 hours until exhaustion. Hypothermia Prevention, Recognition and Treatment suggests not swimming more than 1 km.)