The funny thing is it has nothing to do with blood sugar. You pass out or feel light headed because of the vasovagal response. Eating or drinking just prior to your procedure, within 5-10 minutes prior to the procedure (or just after with certain medical procedures you shouldn’t eat before), will give your brain an endorphin rush that can sometimes short-circuit this response or lessen its effects. Digestion also affects the vagus nerve which stimulates the brain and, apparently, can also lessen the effects of the vasovagal reaction.
Actual glucose serum levels being “low” isn’t really a thing for most people because, generally speaking, nobody getting an implant is actually chronically starving (suffering from clinical starvation) or actually has “low blood sugar”. Unless you’re a massive long term body builder or a diabetic and your insulin dosing is way off, most people’s glucose stores in the liver and muscles will always be there to replenish actual low serum levels for many days after someone stops eating.
It’s just something regular people noticed as a patient or heard from a doctor - eat something prior to the procedure… or they were offered a cookie after or whatever… and somewhere along the line the idea of “low blood sugar” became the layman’s explanation of a much more interesting and complex cascade of effects.
As for the idea of having a fat and protein breakfast vs simple carb breakfast, I think this has to do with time, not sugar spikes. If you’re eating and waiting an hour or more until your procedure, then a simple carb breakfast will be digested rapidly while a fatty protein breakfast will take longer, keeping your vagus nerve engaged longer.