The site is not wrong and it is not my site. It asks you for inputs that seem convenient: rim bead seat diameter spec (622, 630, etc) and tire width (22, 28, 42, etc). With those inputs the code can compute wheel radius in a code unit. The writer shows us how to input the numbers he needs rather than teaching the mathematics. The Wiki article "Bicycle and Motorcycle Geometry" uses radius, but it is trying to show the science.

Sorry for my typing, i'm in a cast due to a broken wrist.

I've taken bike specs from the literature together with my measurements, and run the numbers both on thw site and on the equation, validating against specs. If I use wheel radius, the site result will agree with the equation, with my measurements, and the published specs.

I'd suggest reading Chapter 8 of "Bicycling Science 3rd edition" by Wilson and Papadopous for a detailed discussion of what influences bike handling. It does not explain popular terms such as "twitchiness."

recap:

not my site
site is correct because it checks with my measurements, specs, and calculations
wheel radius is correct because it results in the agreement mentioned above
suggest delving into the Wiki site and the text "Bicycling Science."

What I can't steer you toward is a derivation of the formula based on pure geometry.