Nah it does not work in such way.

Mathematically speaking, even if the mugger can propose an infinite large return in this situation, a kelly better would not bet more than 0.1% (= p = 1 / 1000) of his wealth.

It's very sound mathematics and nothing mystifying.

Edit: A Kerry better thinks in term of a long running sequence of bets. If you all of your wealth just because the game is favorable, you'll eventually lose all of your capital with probability one (in other words, betting everything minimizes the expected value of your wealth in long term). The natural conclusion here is that you need to bet a fraction of your wealth to maximize your long term wealth. But how much? Kelly criterion answers this queation formally. Read the Wikipedia article (or better, read Kelly 1956. It's a good paper) for how it handles the question.