I don't think a compressed video with 4 times as many pixels will be 4 times as large. Consider you already have one pixel of each 2x2 pixel group, then you can predict very good how the other pixels are looking, so you don't need as much data anymore.

The same holds true for images/graphics. Take a look at the (blk) rust logo at several different sizes: https://github.com/rust-lang/rust-www/tree/master/logos

16x16: 351 Bytes; 32x32: 691 Bytes, factor 1.97 from 16x16; 64x64: 1.41 KB, factor 2.04; 128x128: 3.4 KB, factor 2.41; 256x256: 7.29 KB, factor 2.14; 512x512: 10.9 KB, factor 1.50

So it certainly can both hold true that 4K HEVC encoded video has the same bitrate as 1080p AVC encoded video and that it has 50% savings.