That's the beauty of it - the result doesn't require exponential growth (though it does help a bit). If the hashrate of attacker and network is fixed to eternity, the attacker still has a chance of 100% to succeed eventually. This is because the harmonic integral diverges (the cumulative PoW increases linearly, so his probability of success each day decreases inversely linearly. The sum of this goes to infinity and this can be translated to 100% probability of success).
But if the hashrate will not be increasing exponentially, you can prohibit difficulty adjustment patterns that do. 
Though practical fixes aren't needed against something whos probability becomes non-trivial only after life-of-the-solar-system timeframes, which was what I was going for when talking about working out the distribution and not just the asymptotic behavior.