No, its definitely not a made-up thing. AMOLED screens just do that. It is a fact of its design structure that eventually those pixels will degrade and more often than not they degrade unevenly because of the way the screen is used. Cell phones get away with this because most people aren't as sensitive to the burn in, and most of the time the burn in is not very noticeable. With people recycling phones every hear to two years, it makes it even less of an issue because many people trade in their phone or get new ones before any serious burn in occurs.
While I'm bugged by burn in, I'm not letting the AMOLED screen stop me from getting this phone because:
1. 12 month factory warranty
2. After that, nexus protect
3. After that, in extreme cases, I'm sure I could have the screen replaced out of warranty, if I'm still using the phone at that time. To compare, an s6 screen and digitizer is 130 bucks right now. Not too terrible if I'm feeling the 6p for the LONG term.