My understanding is that these are constant current devices since the LEDs are primarily current devices.
If a LED fitting has a fixed voltage to power the device it will then typically have its own driver/s to feed the LEDs…
Yes, especially if you have a string of LEDs. It’s more efficient running it with a constant current supply (as opposed to a series drop resistor, especially for a mains powered fitting) and input voltage fluctuations won’t affect the intensity of the LEDs
Do LED fittings now come with their drivers built in??
I have exactly this happening with some brands of LEDs. When mains voltage is fluctuating, these globes get dimmer and brighter.
But not all of them. As I said, some brands. I haven’t taken an inventory of which brands show this behaviour.
So is that down to the type of rectifier circuit they have built into them?
Well they should have a constant current driver… 
OK… but surely at some point we run into Ohm’s law. You can’t get blood from a stone, and if the power is low, then it is low and since R isn’t changing, V and I will.
That’s how my simple mind sees it.
It’s a sort of stepped fluctuation. These aren’t figures that I have recorded, but they just serve to show what is happening. 230, of course, is OK, 220 no difference… then a bit later we hit 180 and they dim. Then the inverter decides it’s had enough of this, drops the grid connection, it’s output shoots back up to 230 and we’re nice and bright again.