No, that's really not true.
In general, a tree trunk is composed of wood under compression and that same wood undergoes periodical tension when the wind blows. Head leaners are a bit different, in that parts of the tree trunk are always under tension.
When you fell a head leaner in the direction of lean with a conventional shallow face cut and deeper back cut, you are mostly removing the tension wood and placing tension on the compression side of the trunk. This leads to a barber chair event.
By cutting the compression wood out from underneath the head leaner, you are eliminating most of the compression wood, and putting much larger strain on the tension wood. If it fails at that point, the tree does not barber chair, it just falls over. The wood doesn't split, it just breaks off. That is why you place a deep face cut on the head leaner.
The "bore cut" philosophy is to adhere to shallow face cut methodology while reducing the risk of BC. I suppose that is the best way to maximize lumber profits and never break the stem of a good log, but it isn't the best way to eliminate the risk of barber chair.