Turning a light on and off is going to increase the chance of a flood. I have turned lights on and off thousands of times underwater and I have had very few failures. I would not worry about it at all.
I think the advice is somewhat old school and pertains to old type bulbs that had filaments in them. Turning them on and off is more likely to blow the old bulbs. We use to tell people if they wanted to see what a night dive looked like with no lights, press the light head into your belly and it will block all light, rather than playing with a switch.
Blowing a light on a night dive is somewhat of a big deal, saving your batteries in a LEd video light makes perfect sense for a day dive and I don't worry about it at all. kinda like saying,,, don't turn your car off when making a quick stop at the bank, because it may not re-start.. true but probably not something to worry about.