Not sure of the mechanism, but because we are in base ten (10), the 1 represents the beginning of all increases in magnitude. (1,10,100,1000,10000, etc...)
Thus, in any list that measures items is likely to have 1 more than anything else because if you spill over into the next magnitude, you increase the chances of 1 being the first digit by a significant amount. (From 1-99, the chances of 1 being the first digit is .11. From 1-199, the chances of 1 being the first digit is .555, from 1-1999, the chances of 1 being the first digit is .5555... etc...)
So, a 30% chance can make sense. (Increase 1-299, the chance of a 1 is .37, 1-399, the chance is .2775, all the way until we get back down to .111)
The pattern for the rest of the digits in that article bear this out, as well.