That's false. You have to go deeper into the equations.
The results are on Dr. Dave's website and in Byrne's books somewhere, but the basic result is that the cue ball will ideally be going 150% of the cue stick speed just before contact and the cue stick will slow to 50% of its previous speed.
A.D. Moore measured the actual speeds almost 60 years ago and published the results in a paper. He got about 135% for the cue ball speed over a range of stick speeds which tells you how much is lost in the collision (mostly in the tip). Here is the description of Moore's setup from his paper:
The cue and ivory ball were hung by light steel wires beneath a
horizontal 10-inch board. String was wrapped around the ball, and
held in place with Scotch tape. Loops in the string permitted two
wires to be attached. The wires went to screw-eyes put in the edges
of the board, across from each other. Similar pairs of wires (two
pairs) suspended the cue for direct central impact, The vertical
radii were all 20 inches. When both bodies were at rest, they grazingly
touched.