I got the impression from that section that it only applied when doing overland movement. That when you were travelling in "exploration turns" you had to declare what actions you were taking and making a map meant you weren't keeping an eye out for threats. Which makes sense to me.
However, I didn't think it applied the rest of the time. So if you were in a dungeon and walking down the corridor that you got your passive perception on all secret doors you passed and all monsters that tried to sneak up on you.
I can't imagine telling my players "Sorry, you were looking at the map so you didn't hear the monster sneak up behind you." Someone would say "Does reading a map suddenly mean my ears stop working?" and there would be an argument over it.
I don't get that impression. If your attention is turned to something else, then it's not on noticing hidden threats. That makes sense to me. Why should there be a difference between keeping an eye out for hidden threats while travelling and any other time? If I'm rifling through the heap of broken furniture searching for treasure, I don't get to notice the giant spider sneaking up behind me. But the PC who opted to keep watch while I did that might. There wouldn't be an argument over this at our table because the players are aware that mechanics are only brought into play when there is uncertainty and the DM determines whether or not there is uncertainty.
Edit: I will add that treating it this way creates a meaningful choice during play instead of just a matter how much a player chooses to pump Perception during character creation and advancement.