I'll comment on the article first, which if you ask me, seems like some jokester had written it.
If not being used for a prolonged period of time, laptop Lithium-ion and Ni-MH batteries should never be completely discharged before prolonged storage
. Fully discharging a Li-ion battery before storage can activate the protection circuit on the battery as it naturally self-discharges, which will render it dead (as Li-ion batteries are highly unsafe to use if the voltage drops below the safety threshold). However it's safe to run the battery capacity down during normal use, as long as it's not left at 0% capacity for a prolonged period after (that is, it's fine as long as you charge the battery soon after).
Ideally, they should be charged to around 40% charge level
before being stored in a cool, dry place. The lower the temperature the better. The best place to store Ni-CD, Ni-MH and Li-ion batteries is in the refrigerator in a bag (but not the freezer). These conditions help reduce diminishing capacity over time.
As for leaving the battery in the laptop all the time, nearly all laptops these days will charge the battery in a smart fashion, turning off the charge when the battery reaches full capacity and switching to AC power. Personally, because I'm always taking my laptop places, I always leave my battery in my laptop (even when it's fully charged) because it's more convenient for me.
...However, it is not good to keep the battery fully charged all the time
(and so always connected to the laptop) because prolonged high voltages promotes corrosion within the cells, which over time will decrease the effective capacity and lifespan of the battery. In addition, heat from the laptop itself can help promote a decrease in the effective capacity of the battery (especially if it's a laptop with poor thermal design, or where the battery slots into a concealed compartment).
Here are some good places to go to learn more about Laptop Batteries:
Hyperzone!: Power That Laptop!
Battery University: an on-line resource that provides practical battery knowledge