I hate to say this, but you ARE supposed to remove a LiION battery from a device that is running on AC power. It's bad for a LiION battery to be run fully charged at a high temperature, which is exactly what happens when you leave the battery in while running on AC.
Here's a good link about proper care of LiION batteries. Contrary to popular belief, you DO have to excercise a certain amount of care to prolong lifespan:
How to prolong lithium-based batteries
And here is where good information is applied improperly to a situation and makes it bad information for the subject at hand.
First and foremost that particular article was written for laptop batteries and their charging systems. Which differs greatly from cell phones and how they are setup.
Lets break down some significant differences between the two.
1) Cell phone's battery charging systems switch to trickle charge mode no later than 4.00 Volts. 4.01 volts is considered fully charged.
But wait! The article says "4.2V" is fully charged. And they are 100% correct, but cell phone makers know you will leave the phone plugged in over night and that can be for as long as 16 hours for some people.
So why do they go into trickle charge at .2 volts to soon? To protect the anode from oxidation which causes resistance in both the discharge and charging situations. Plus they don't want the battery to fail prior to the warranty expiring.
If you want to have fun, read up on "Bump Charging" for cell phones if you want to understand why the charging circuits are designed to kick in to trickle charge earlier than 4.2V. And how bump charging can get around that and give you "Extra power!" at the cost of battery longevity.
2) The trickle charge mode isn't high enough to sustain a full charge if you are truly putting a load on the phone.
If you care to test that fact, put your phone into GPS mode while using 3G to retrieve the mapping data. And if you really want to see something neat, turn Pandora or a similar program like that on at that same time and watch the charger not be able to keep up when it switches back to full charging mode. Some car charges use lower currents and can't keep up.
3) Cell phone batteries are smaller than laptop batteries.
Li-Ion batteries can reach "Thermal Runaway", a form of self heating, at temps as low as 140F. But if you read every word in the article it talks about temps of 113F. There is a HUGE reason for the difference in temps and warning about them. Cell phone batteries can dissipate heat faster than laptop batteries by a factor of, lets go with 20 to 1 (it is probably much higher). Why is the difference that high? Surface area exposed to cooler air. Laptop batteries simply can't dissipate the heat fast enough. So they have to start worrying about heat build up long before cell phones do. That and the fact that they go to the FULL 4.2V charging spec. Which is the danger zone for oxidation of the anode.
So in short the article is 100% correct for a Li-Ion battery of large mass being charged to the full 4.2V specification.
Cell phone batteries don't meet either condition. Not by a long shot.