He's not saying that health insurance is related to the stock market. He's saying health insurance is going to keep becoming more costly until a proper solution is found for the US health market. In the mean time, it's unsustainable and the premiums increase every year. Therefore, even a run up in the market might not be able to compensate for the unanticipated cost of health care. In other words, 25x your annual expenses may only be 20x in the future, for example.
But the 4% rule already factors in inflation. Are you saying health costs increase at a faster rate than inflation? That may be true temporarily but can't go on forever.
Well, yes, that's exactly what I'm saying. ACA premiums increased 25% last year alone, obviously well beyond inflation. You're right, the market will level out at some point. But if your FIRE budget was designed around 2014 health care costs, 2020 health care costs are probably going to be much higher. Therefore, your budget will need to be higher.
The only reason why this is a problem is that healthcare is a relatively large percentage of most mustachian's basket of goods. Most of our budgets are so refined that a large bump in cost of a particular item disproportionally affects our perceived inflation versus total inflation.
For example, you start to notice that your grocery bill is ballooning due to the increasing cost of your nightly steak. Easy, change to having nightly chicken instead which has gone done in cost. While total inflation remained steady in the steak/chicken economy, the two sectors did not (but they balance out).
Unfortunately, there's no chicken healthcare that's an alternative to the ACA or whatever it becomes. There are limited options for health insurance out there. And with the insurance companies struggling to make ends meet with the new rules, they're charging more just to survive.
http://fortune.com/2016/10/25/obamacare-insurance-premiums-2017-healthcare/