For SINGLE Cell Li-ion devices:
There is no reason that charging a Li-ion battery up the first time before playing with your new device, would in any way extend the life of the device or the battery.
The simple fact is properly stored lithium-ion batteries are charged to about 50%, and lose some of that charge (depending) while sitting around in the package, or being shipped. So properly treated the battery will have less than 50% charge when you get it.
Why are they recommending or even insisting on getting you to charge?
Because when you first get a device. you spend a long time configuring it and testing it. When you first test the device it gives you a "first impression" of the device. The battery WILL run out. Running out sucks :-)
Because almost every Li-ion device sold has a protection circuit to keep the battery from dropping too low in voltage, there is no reason to enforce this policy or worry about it other than, It is going to run out, and you will be unhappy.
If when you get your device, the battery voltage is so low that your device will not operate, you should definitely charge the battery, before leaving it in said device. The battery should not have come to you in that condition, and would be a suspect battery at that point. The low voltage protection could have saved it mostly still anyway.
How bad the battery would be at that point could vary from totally usable still, to completely unusable.
This all changes slightly, and gets more confusing with higher voltage Li-ion batteries.
SERIES: With laptop batteries
it can be more important to charge before use, because a proper charge circuit could balance.
This all gets very complicated and muddled. A "proper" circuit for series Li-ion would not ever allow any cell in the series to get so low in voltage that it it could damage a battery.
Fact is. there are improper circuits out there, that do not monitor Every cell in the battery pack. But often those same poorly done battery packs and charge systems will not have balance either.
So there is one type of series pack style (no individual battery cut-off) that it would be far better to charge it first before using it. Under very specific situations, with this one type of semi-proper system, it could damage cells permanently to a small or large degree, even on the first "way too low" discharge of a single cell.
Other non reasons: To calibrate the Battery, While many devices have a specific Ma usage metering capability in the chip, there is no reason that charging it then or later would change that. Again even if the battery uses this kind of "info lithium" or "smart" capability to determine battery fill, there is still (usually) protection that would keep the battery from being damaged.
Some of it might come from older battery types like Ni-cd and Ni-mhy where a full charge is way more helpful, And can balance out a series set of batteries prior to discharge. This keeps the battery set from reverse charge.
Because Li-ion (every one) is supposed to have protection, and also should be balanced on charge, it does not balance the same way Ni-. chemistry can or do.