[jjoonathan]

It's mostly a philosophical conundrum, not a practical one.

For any given definition, there are a handful of possible "defining experiments" being carried out at a handful of national labs. Their deviations with respect to each other are constantly being monitored and metrologists are constantly chasing down error terms. Yes, they choose one standard to "bless" as the official definition, but it's their job to live below that abstraction and to maintain it. If their "blessed" definition started to drift with respect to the other candidate definitions they would notice very quickly and react appropriately. The fact that most of us entertain a single definition isn't a consequence of philosophical confusion as to whether or not one exists, it's a consequence of delegating the ongoing experiments backing our simplifying assumptions to a group of people who are very good at them.

For instance, the disagreement between solar time and atomic time is monitored so closely that the slowing of Earth's rotation due to tidal forces is a gigantic signal compared to measurement noise:

https://en.wikipedia.org/wiki/Leap_second#/media/File:Deviat...

If, say, Earth flew through a cloud of dark matter that somehow messed with Cs absorption lines, we would see Cs clocks drift with respect to Rb clocks, unlocked quartz clocks, Earth rotation, Optical Lattice Clocks, etc, etc. The event would not go unnoticed. Cs clocks would be demoted from their position as primary time standards and the next best candidate would be promoted.

[xgk]

   somehow messed with Cs 
   absorption line

In a simple case yes, but if all other time keeping mechanisms would also be messed with by dark matter, there might be no way of saying which one is the right own.