Absolutely correct Bill S => beam will strike the observer at c-v flight time [it's Bill 6 not Bill S]
BUT
the speed of light was c throught that whole thing it was never travelling at c-v anywhere, closure speed IS NOT the speed of light.
On the basis that the beam of light strikes the observer at c-v it must have previously approached him at c-v.
No observer will ever see that c-v speed, he is showing the speed of light to the moving observer and everyone else is still c.
In his book 'Relativity' where he deals with the Relativity of Simultaneity Einstein writes that from the stationary observer's point of view the train passenger is hastening toward the beam of light coming from B whilst riding on ahead of the beam of light coming from A.
Contrary to your comment that no observer will ever see that c-v speed, the stationary observer of Einstein's RoS depiction 'sees' beam B as having a rate of closure of c+v relatively to the passenger and 'sees' beam A as having a rate of closure of c-v.
He 'sees' beam B moving toward (having a rate of closure with) and reaching/striking the passenger at c+v and beam A moving toward (having a rate of closure with) and reaching/striking the passenger at c-v.
