If the label shows less than 1g of carbs there is probably very, very little honey in it. Just enough so they can claim it's flavored with honey to make it sound more appealing? I can't see how the diet tea is spiking your BG. Not sure about the warning they put on the bottle about diabetics, though. Maybe a CYA thing?
I've never had BG spikes from any diet drinks that contain aspartame or sucralose (Equal/Splenda). I've had some diet teas that do contain minimal carbs from fruit juice, just a garm or two, and I don't even think about those.