If I understand it correctly, this paper:
https://bitcoin.org/bitcoin.pdfon page 8 argues that the probability of an attacker generating an alternate chain depends on the number of confirmations (z), not on the time between confirmations. Is the analysis wrong?
I believe that paper is referring to the likelihood per attack. If the attacker has 10% hashrate and confirmation time is 4 blocks, they have a 1% chance of a successful brute force attack. If there are ~10,000 blocks per hour, they could have thousands of tries.
The first results at the top of page 8 would be the case of an attacker having 10% of the total hashrate. The calculated result is that if you have four confirmations (z=4) then P=0.0035, i.e., the probability of a successful attack is 0.35%. With six confirmations the probability of a successful attack drops to 0.02%. With ten confirmations the probability of a successful attack is 0.0000012 or about one in a million.
Note that this is independent of the confirmation rate. You can make the confirmation time as short as you want, and the analysis is the same.