S/He obviously has some server side scripting going on which will serve up different code, depending on the browser used to visit the site. This means that using IE to always visit the site may not download code that breaks another browser. One option suggested was to use extensions in Firefox to pretend to be another browser. I've seen many instances where that doesn't always work.
Personnaly, I just install the various browsers on my machine (or several if I have to), keeping one browser as default, then visit the site with each browser and view the source code from there (save it if you need to study it later). If I need to check different/older versions of each browser, I use another computer with it still installed. And, I ALWAYS check each page in each browser using different screen resolutions just to see if the page layout converts properly.