I didn't watch the video, but I don't see how that could be true. Occam's razor is about complexity, while the conjunction fallacy is about logical strength.
Sure 'P & Q' is more complex than 'P', but 'P' is simpler than '(P or ~Q)' despite it being stronger in the same way (P is equivalent to (P or ~Q) & (P or Q)).
(Another way to see this is that violating Occam's razor does not make things fallacies).
The actual quote is:
"...which of course violates the conjunction rule of probability theory - also known as Occam's razor - which says that a more complicated event cannot be more probable than an a strictly simpler event that includes the more complicated one."
41 minutes in.
Link.
"Razib Khan has an academic background in the biological sciences, and has worked for many years in software. He is an Unz Foundation Junior Fellow. He lives in the western United States."
Razib's writings can be found on his blog, Gene Expression.