Tire Rack's statement is correct but refers to new rubber. A slick tire has the most grip and a shaved tire will also offer more grip than a comparable tire with full tread blocks. That all assumes new rubber. A tire worn down through use to the same tread depth as a shaved tire will not offer the same grip. Doesn't mean you can't use it, just be prepared for a potentially very slippery feel. For your first track day it should be fine.
16 GT3 | DBM