Which it may be, in very rough terms, ....for a main parachute, including typical operational factors that don't involve the design itself.
Reserve parachutes are probably an order of magnitude more reliable. At least that, I hope.
Reserves don't get packed in 5 minutes before the next load, with lines with 800 jumps on them, so there are operational reasons for improved reliability. That's in addition to the much more conservative design than used for the faster main parachutes.
That still doesn't get to the one in a billion you were talking about, but whatever the stats are, it is regarded as safe enough. Especially when there are so many more ways to die, so many more things to watch out for, that failed reserves are a tiny, tiny fraction of all skydiving fatalities.
That makes sense. Thanks!