I share the ops questions, and I don't feel it's been fully answered yet.
If you are flying through air at a constant pressure with the altimeter set properly, at standard temperature, then indicated is showing height above that altimeter setting, which could be 29.92, standard datum plane, or some other setting which is assumed to be mean sea level. Thus indicated shows MSL.
Now as you fly and maintain indicated altitude, you fly into colder air.
The rote rule, which I'm fine with, is that indicated will stay the same, but MSL will be lower. high to low, look out below.
Just how can you possibly be lower, if the altimeter itself didn't change? In this case, it must start to trend down slightly, so you follow it, thinking you are still at the same MSL altitude because it's still indicated, but you're actually lower.
After all nothing else changed, but temperature, and the airplane is flown at a lower MSL than indicated.
Looking at the inverse, say you stayed at the same true altitude (somehow, using a different instrument), then the altimeter would trend down, but you wouldn't follow it, and it would thus show it's errors.
Perhaps the problem we're having is trying to mix high to low, low to high concepts with density altitude concepts. I would be happy if this was true - the altimeter changes a little bit with temperature, it tries to ignore it, but doesn't completely do so. And we as pilots much understand this.
But density altitude is a calculation that is not at all trying to ignore the temperature's effect on altitude. If altimeters did account for temperature, they'd show you density altitude. And you'd have great insight into your aircraft's performance in real time, but you'd have no real clue what your true altitude is.
So calculated density altitudes at one spot are going to be possibly much different than the muted indicated errors on that same spot. But, the errors and density altitude will move in the same direction.
Please feel free to reset my thinking, if it's way off.