That is a mistaken notion. The half hitch is nominally stronger than timber hitch, since it is only doing a 90° bend. The Timber hitch starts off at a 180°. As we all know, the tighter the bend, the sooner the rope breaks. It also spreads out the shock load on the rope to two different areas, since the 1/2 hitch only takes part of the load. It passes quite a bit of load down to the timber hitch and the friction going around the log, so it's considerably stronger if you have a possibility of breaking the rope.
But more than that, a half-hitch secures the rope better against any log rolling or the loop sliding off the end if it doesn't set securely before the weight binds the log to the loop of rope. If you are working with a short but heavy log, you should abandon the timber hitch and use a Stilson hitch. I'd guess any time the diameter is greater than the twice the length of the log, I'd not trust the timber hitch to hang on in a fall.
The knot shown in the video is a bit different than I tie. The Buckingham port-a-wrap manual shows this knot:
View attachment 1162974
Mine isn't quite the same as this either, but quite similar. Having studied the diagram above, I think this is a pinch more trouble but better than my version.