You might think that, but the law actually currently uses a concept called "portal-to-portal". Companies only need to pay for time that is "integral and indispensable" to the labor in question. In short if you aren't actually earning money for the company, they don't necessarily need to pay you.
It originated with mine workers who would have to take a long mine-elevator ride (30m+) to and from the vein, and companies didn't want to pay for that time. They successfully argued that the time spent riding the elevator was essentially part of your commute, just like driving to work, and they shouldn't have to pay for it.
Lately it's also been applied to things like Amazon warehouse workers, who need to stand in line for up to 30 minutes to go through a metal detector and be frisked on their way out of the warehouse. That time is legally allowed to be unpaid.
In short - even if the work is in some sense "necessary" as a condition of your employment (you would be fired if you didn't wait through Amazon's frisk line), if it's not actually a primary part of the job (the thing they are paying you to do) then they don't have to pay you for it.
The FAA may mandate downtime, but that's not part of worker safety per-se. Consider if the pilot were taking that downtime on the ground - you obviously wouldn't be paying them to do that. Nor would you pay a long-haul trucker taking their downtime.
The company could argue that the "portal" in this sense is the cockpit door (rather than the door of the plane), and that being trapped in the plane during your off-duty time is just an unpleasant aspect of the job (like a miner being trapped in a mine elevator during some of their off-hours). You're perfectly free to watch a DVD or whatever [0] so you're not really on-duty.
This is a pretty shitty thing in labor law overall, but as a descriptive statement - that's how things are right now. If the wheels aren't turning, you ain't earning.
Or at least if you're earning it's through the grace of your employer, not because they're legally obligated to.
[0] Interestingly enough, the FAA doesn't actually mandate sleep during off-hours. Which is a big problem since many pilots are paid so poorly nowadays - they end up flipping burgers to make ends meet, instead of getting the sleep they need. It's caused several crashes so far.