Are you sure they do not go to sites at the domain apple.net (which is not an actuall Apple domain)?
Regardless, as you know the email is wrong, your spidey sense should be tingling like 10,000v charge.
My rule of thumb for any email that you are unsure of, is do as you did and independently verify the information yourself. As you checked on your device, without using anything in the email itself, that your storage is fine, clearly the email is at least flat out wrong, and almost assuredly a phishing scam.
Apple may warn you if your iCloud storage was full, but I doubt they'd bother to check your actual usage to two decimal places and send that.