Not true -- though you only get the warning when it happens inside cultural borders (I think).
I'm sure I've seen a forest grow just outside my borders. I -know- I've seen a jungle grow outside my borders (one turn that rice over where I want my second city is on a grassland, and when I come back later, it's in a jungle! I played around with this start several times, and I kept an eye on the rice, noticing it being sometimes being in jungle, and sometimes not)