your google android phone has a built-in calendar that is linked to the account set up on your phone (gmail). you can update the calendar on your phone without having to sync on any other devices or on any web server. many widgets will use the stock calendar app and just make a nice widget on your desktop. in essence yes it lists your gmail account as its "account" but only to differentiate between calendars in case you want two different calendars since some people dual-gmail.
do you not like the stock calendar?
if you dislike the stock calendar then you want to search for a full-fledged calendar app and not a widget. quite a few give you the option to sync with other accounts if you wish but i've seen a few that are entirely self-contained.
i'm having a hard time remembering but i think "grid calendar" might come with its own calendar app, but dont quote me on it.
Imagine i lived in the outback, no service anywhere, i dont know what google is. somehow i have a smartphone. I would like to organize the next month with a calendar app that doesnt ask me what my email account is because i dont have one.
when you buy an android phone setting up an account is the first thing they do. you need this to access the marketplace.
if the calendar is asking for an account then the phone was not set up right. you might be missing out on a few features that the rest of us take for granted. keep in mind that just because you have an account it doesnt mean that your phone will always sync the two or remain tethered to the internet. for the calendar its more of keeping track of which calendar is which (in case you have multiples) or syncing (if you want to only)
if however you dislike the stock calendar (which works fine off the grid) and would like another calendar completely seperate... i gave you a few options to look into.