Yes, that write-up is absolutely correct. Since each weapon is being checked for proc activation each time they shoot, the chances of any proc activating does go up as more weapons become involved. You can use the binomial formula below to get exact numbers:

http://www.stattrek.com/online-calculator/binomial.aspx
For example, if you shot a single phaser turret at a target, the odds of getting a proc is exactly 2.5%. If you shoot 8 phaser turrets at a single target at the same time, the chance of any proc activating is raised to 18.33% where Cumulative Probability: P(X >= 1). You will NOT see this by mousing over a single phaser turret involved since this is a cumulative probably taking into account all 8 phaser turrets shooting together.