But why would they also offer a recommendation for the 40 grade and qualify it with the 'for improved vehicle performance' phrase?
Drivers handbooks are not usually written by engineers and their choice of language is often poor, even misleading. A heavier oil grade does not improve engine performance in the slightest; quiet the contrary, it saps power and fuel economy. What it may do is possible reduce oil consumption under constant high rpm and high oil temp' usage so I guess you could consider that "improved performance".
The thing is both the 5W-30 and 5W-40 grades are recommended for unlimited maximum oil temp's. Here in NA it is the 5W-30 grade
that dealers use and of course running the 5W-30 grade, even a dino 5W-30, will not in any way void you warranty.
The engineers have set the engine management safety systems based on the lightest grade recommended which is 5W-30 consequently there is no lubrication benefit in running the heavier grade.