Earlier quoted context omitted.
They also finally cashed in the 'big side vs. small side' credit they've been holding onto since they first branded HD (720 and 1080 are the (exact) pixel-lengths of the small sides, while 4k is (less than) the length of the big side). Edit: Not only that, but they can (defendably) make the claim that 4k is "4 times the size of 1080p" while (deniably) knowing that some people will misinterpret.
Misinterpret how? By expecting that the sides will be four times larger? That exists, and it's called 8K. "Megapixels" already exists as an entrenched concept, and I don't think it's deceptive to call 4K 4x larger than 1080p or 8K 16x larger than 1080p.
1080 = 1080 vertical pixels
4k = 4000 = 4000 vertical pixels? Nope.
Shit's confusing. 2k or 4x would be less confusing.