Yep, that works. Is the Flash movie not showing up at all, or do you have problems with subsequent loadMovie() commands?
If you have a base tag, use this format: <base href=""></base> not the short form <base href="" />. Sometimes it seems like this is causing problems.
Also, post a link, if it’s online. And test with more than one browser (although swfobject works in every browser worth mentioning...)
Since your site is located under /mysite folder, the absolute URL should be /mysite/assets/flash/file.swf
The easiest way to rectify this issue is by using <base>, as suggested by others. If you have <base href="http://localhost/mysite/">, then your URL would be assets/flash/file.swf.