Sorry, I don't see the connection. Yes, a successful candidate is worth a lot of money to Kalzumeus, and they are incented to make sure that the solutions are real and not plagiarized. But that salary is worth even more to that successful candidate, and hence they would be willing to pay handsomely for someone to write customized, non-plagiarized solutions for them if it gets them in. (The mythical level 45 mentioned would cost $44K. If I'd done the math, I probably would've made it more. I guess the level 52 would be nearly $750K...)

For now, I'm assuming they have good protection against automated solutions. If it were just a matter of detecting plagiarism, you're right that it would be trivial. (Heck, I even cofounded a company that did code plagiarism detection, so I have a very good sense for how easy or hard it is. tl;dr: it's straightforward to defeat a plagiarism detector if you are sufficiently motivated and knowledgeable and willing to put in some time to go through all the code, but people/companies who plagiarize are typically none of those.)

Detecting whether someone else is doing the candidate's work, on the other hand, is impossible. Unless you bend the rules. Fortunately, the rules seem pretty pliable to me -- when a candidate arrives at a company's interview, spot-check them on their understanding of a few of "their" trickier solutions. It's a logistical nuisance, to be sure.