GoKawiilAt first glance, the claim seems a bit absurd: how could a 1080p image look better than 4K, a resolution with four times as many pixels? Resolution tells you how many pixels are on the screen, but it doesn't tell you how much picture information survived compression before those pixels reach your TV.
Streaming services, for example, have to send all of those pixels through an internet connection; to avoid buffering, they compress the video. Your TV or streaming device then decodes the compressed video stream before it reaches your eyes on the display. But "decode" is not the same thing as "restore." The process of compression, sending and decoding demands a price, and that price includes discarded details like fine film grains, shadow transitions, texture details or complicated motion information.
The differences are usually easier to spot in difficult scenes filled with smoke, rain, moving leaves, huge crowds on the move and deep shadows. On the other hand, a 1080p Blu-ray preserves those same details more naturally and presents them better than a lower-bitrate 4K stream.