Max health is the best, even if not always necessary, but just "alive" isn't good.
When the tanks are low health, they might trigger their longest cooldown or check closely what's going on with the healer in case they are attacked by surprise or something, leading to unnecessary distraction or avoiding they pull yet another annoying mob.
In a PUG, you might be a good healer, the tank doesn't know it (yet.) They'll know it near the end, meanwhile show you can make the tank happy.
Agreed. This guide is written with the worst case scenario in mind: 3 or 4 players that have no clue how to tackle challenging group content and do not have the gear to make up for it. Keeping the tank at max will enable him to be more relaxed and hopefully perform better. If they can't handle stress, that's when you wipe. Is it the tank's fault? Probably, but can you blame him? He just doesn't know what to do. Setting out baseline rules can help this "Worst pug ever" into a semi-succesful group.