jquery.js from CDN sources
No, Drupal devs didn't rewrite jQuery, a standard version is included (1.3.2). I can vouch for flag.js working fine with that version of jQuery.

It's not compatible with the version of jQuery that you're including though. You're probably also introducing a conflict between the two versions of the library that are included in the page.

jquery_update isn't a huge module at all, and it gives you several versions of jQuery plus the CDN option out of the box. It was written specifically to solve the problem you're trying to get round.

There's no good reason not to install it; if you don't, you'll just be reproducing functionality it already provides, which is time you could spend doing something productive.