"The statement is true, however, if you think of the starting point as say a beam reach. As the apparent wind goes forward and accelerates you are able to trim and power up. "
This is very important because you have now added the element of actually going somewhere.
Very rarely are we interested in simply picking the best point of sail (best speed). Usually we are trying to go somewhere. So we try to point the boat where we want to go, set the sail and then the boat accelerates and we trim.
Here's how it can trick you.
In scene 1 the sailor is trying to go to the destination
X. He is on a reach and the true wind and apparent wind are not the same. What he sees in the wind indicator is the apparent wind. He thinks he can come abeam the destination
straight for it on a close haul.
In scene two he has made his tack and is confused why his sails won't fill. He has to continue bearing away until scene 3 and now he is not headed for his destination.
This still may be the fastest way to teh destination but he is now beating to windward and will have to make a couple of tacks. Alternately he could have sailed a lot closer to the wind in scene 1, pass the destination and make maybe one tack.
Usually when I get to scene two It is the end of the day, everyone is tired, I realize what a dummy and bad planner I am and fire up the iron sail - LOL