I think there's a misunderstanding here. According to the article GPS uses atomic time, which is not subject to leap-second corrections. UTC is subject to leap-second corrections, because it drifts from atomic time.
Coders over the next few decades began pegging the clocks of various software programs to GPS system time, not Coordinated Universal Time—the one that gets tweaked by the occasional leap second.
Moreover it says...
Every time there is a leap second, that information has to be changed in the GPS message. In other words: It’s a window of vulnerability
Only IF the GPS system is not adjusted. It's a risk but it's a risk that has been, and is being managed.
Remember also that GPS does not allow pilots to LAND blind, there is still a requirement that a pilot has to physically SEE a runway before he can descend below a certain altitude (which is published seperately for each airport, though AFAIK it's generally around 400 feet above the ground, it may go as low as 200 feet, I'm not entirely sure). That is why airports can still get "fogged in" even though GPS exists... Pilots are not taught to trust GPS explicitly, since it can be slightly off even in great conditions, and if it fails they must still be able to fly and navigate. Moreover GPS is not the primary system that gets a big jet down to the runway in foggy weather. It can help you navigate but beyond finding the airport or getting more-or-less lined up it's of little use for precision work. That part is handled by ILS
People over-estimate the importance of GPS in a cockpit, even big modern computerised planes can still be flown completely without it.