That’s true of lights that use FET drivers to achieve high output, which is the case for all budget lights.
However, lights that use boost drivers can suck more current out of a low-drain battery than is safe. For example, my Zebralight SC600w MkIV Plus has a “turbo” mode of 2300 lumens. It uses a boost driver for regulated output, so it produces 2300 lumens regardless of whether the battery is low-drain or high-drain.
I can use an old low-drain laptop 18650 cell in it, and it runs fine at 2300 lumens. But the battery heats up quite fast, and gets pretty hot. (This is not the case for high-drain cells that can sustain higher currents.) I think it’s drawing around 8 amps from the battery, where it’s only rated for 4 amps. That explains why it gets so hot. I wouldn’t recommend doing it for long. The light’s thermal controls will kick in to ramp down the light eventually, but that detects heat in the driver not in the battery.
For FET drivers and linear drivers, that is not a problem. The battery’s voltage sag will cause the output to drop right away, and limit current.