No, it's not wrong or we wouldn't be finding 5K year old instruments underneath melted glaciers as this article's evidence shows. And ice core samples from Greenland and Antarctica support this.
Glaciers don't melt instantly the moment the temperature flips from "form glaciers" to "melt glaciers". They operate on the integral of temperature -- heat. The temperature determines how fast they melt or form.
These melted really, really fast.