The website is down so I have no idea what his argument is, but when I studied the concept I found it alarming they just handwave away the issue that it depends what Turing machine you use. There's no reason the constant can't be arbitrarily huge.
If it helps any, the concept of KC is so impractical that this is probably the least of our worries.... The main important thing is that any theorem you prove will hold no matter which programming language/Universal TM you choose.
How doesn't it? It makes it completely impractical to use because the complexity you get for any string is entirely dependent on the language you use. We have no way of deriving what function set the universe uses from first principles.
Just as for any finite string you chose you can chose a finite language L to trivially produce it, for any finite language L you chose, you can chose a finite string S that can't be trivially produced. If you chose L such that it trivially covers the structures of one universe (or a finite number of universes), there are infinite other universes in the same class of complexity which it doesn't cover.
