It would perhaps not be very wise to assume this is a false positive. Equally or perhaps more likely that it is new malware that other companies have not added to their definitions yet. Kaspersky are pretty hot when it comes to nailing new viruses.
It won't hurt to turn off your virus protection while doing a scan as long as you only have the one instance of your browser running and don't go downloading files from another site at he same time. But you knew that anyway, didn't you?
You should always have your firewall up and not lower that for anybody.
Online scans are a useful double-check, and some will even remove malware.
I've compiled a little list for anybody who's interested:
http://www.geocities.com/dontsurfinthenude/antivir2.htmsee:
Online disk scanning
