Unless it's changed since I last used it, Symantec's online checker (like many if not most online scanners of this kind) needs IE because it uses ActiveX. It downloads an ActiveX component (which is a amall program really) to your computer to do its thing.
ActiveX allows websites to do cool things however if you have it completely enabled (not set to prompt where at least you can choose whether or not to let a site run an ActiveX control on your PC although that can be a pain when you get a lot of prompts), that means any site you visit can use ActiveX to put stuff on your PC without your knowledge. Which is how a lot of spyware gets on PC's. (Also javascript can also be used to load exploits through the browser.)
Some of the newer known IE vulnerabilites, not entirely yet patched by MS, can allow exploits if any scripting is enabled. Of course you'd have to actually run into a site that has such exploits on them. But a recent incident where "good" sites (which were not publicly named) had their servers compromised and included a malicious script that apparently planted a keylogger on visitors' PC's showed that it's not just going to known "questionable" sites that can result in problems. http://zdnet.com.com/2100-1105_2-5247187.html?tag=zdfd.newsfeed While MS issued a patch, it reportedly doesn't really prevent these sorts of exploits and the recommendation is to disable all scripting, including javascript, while using IE. Bummer. >
Anyway, just be careful out on the WWW.