Only been 15 of these in the modern era (post 1900)
Indeed. While a no hitter can be completely in the hands of a pitcher a perfect game also depends on perfect fielding by the teamates so they had a hand in the result as well. Some luck also can play into these things. Last night on the radio someone said Johnson on a few pitches narrowly missed hitting some batters legs or feet.
I was looking over the list on mlb.com and 8 of those have come since I was born (1967). I think this is in part because big league hitters try to hit more home runs now and strike out so much more than in the past. There is less focus on putting the ball in play, and so it is less likely for a poorly hit ball to find its way through to becoming a hit.