I'm not doing a very low carb diet per se, but the amount of carbs I eat per day varies a lot (anywhere between something like 30 and 150, I think). Which means the amount of insulin I take varies a lot as well. I guess if you are confident adjusting insulin to food it shouldn't be dangerous. Basal insulin need might change too on a low carb diet, as may your ratio's. Again, if you're fine adjusting your insulin I don't see why it would be a problem.
The other part of the supposed danger is ketones. Should you go low enough with your carbs you'll develop ketones. Normal starvation ketones, just like when people haven't eaten for some time. The problem is that with T1 ketones are usually very alarming.
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@Mel dCP , I think she eats pretty low carb.
Good luck!