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.
Using the vertical line count is a legacy of CRT displays and analogue connectivity/broadcasting where there was no horizontal pixel count only a maximum frequency due to the nature of the technology. There were 1080i CRTs so it is only for the next generation it is possible to change to the terminology used in cinema and professionally for some time.
Every pixel on a 1920x1080 display is replaced by four pixels on a 4K display so I'm not sure a "4 times the detail" type statement is particularly wrong or misleading. It just doesn't derive from 4000 = 4 x 1080 type logic.
The 4k confusion comes from the decision to simply double 1080p for consumer equipment instead of going the route cinema is going with true 4k horizontal resolution and still co-opt the easy 4k name.
And really, who wants to walk around saying 2160p? Makes me want to follow up with "1.21 gigawatts!"
I do agree with a statement in an article posted here about 4k a few days back. At this point the cinema guys should toss in the towel and just use the term 4K PRO and let consumer equipment use 4k.
You and I can be bitter about it all we want, but there's no point.