What they are talking about is reducing sidewall flex by using larger wheels with the same overall height. This reduces the height on the sidewall. That prevents the sidewalls from rolling over as much because the sidewalls are stiffer. It allows the driver greater confidence in the vehicle because the contact patch does not change as much and there is no (well, much less) sideways motion from the tire waggling on the wheel. Also moving up in size creates a 'flatter' contact patch which helps improve braking and acceleration as on smaller wheels the tires are rounded more for the same overall height.
I don't think that this is universally accepted as being true, i.e., that shorter sidewalls improve handling, despite the book citation. Carroll Smith's books disagree, and I've seen a lot of opinion from reputable sources that the opposite is actually true. I suppose it's no mistake that some of the top racing series (e.g., CART, Formula 1, NASCAR, etc., etc) tend to only use wheels just big enough to clear the brakes and wind up with high sidewalls. FWIW, from a performance perspective as far as I can tell that's the main reason to use a bigger wheel: to clear bigger brakes. If you're not going to make use of the additional brake clearance, the larger diameter rim may actually wind up hurting you more than it helps, especially on a car with McPherson struts that doesn't have a favorable camber response (e.g., a SHO).
Sidewall compliance can work to your benefit, e.g., by helping to keep the tire on the ground across the section width...this helps keep the widest contact patch which has the benefits listed in the book citation.
Consider also that the some of the stiffest sidewalls out there are on run-flat tires, and they're not known to be that great for handling. People take those off for track days/autox and put on something with more compliance. I don't think the "stiff sidewalls are better" argument is really true.
Whoever is giving you this information is not well-informed themselves.
I suggest reading a lot more on the subject if you want to become a better driver. A good place to start is
The Physics of Racing Series, google it.
EDIT: By the way, that's a pretty sweet looking car.
The Physics of Racing series is excellent. There are a number of other good reading references, too, like Bondurant's book or other driving books (I have a pretty good library of driving/race engineering texts...they're definitely worth the investment if you're reasonably serious and especially if you do your own wrenching).
And with those suspension mods your considering installing, your SHO will handle like no other.
Anyway, I have a picture of the page for the book I posted above. Basically what it says is:
