'but a virus is a virus, so there can be no mistake here'...sadly this is not the case. Virii can be hidden easily and no amount of detection will see them. They can be entwined into HTML coding and will be invisible to scanners UNLESS they are executed. OTOH many ISPs do have basic virus protection but nearly all virii are harmless but annoying, so there is litle to worry about. the scare stories about virii are largely apochryphal with huge doses of Aesop. Self-responsibility and regular updating of your AV will be sufficient.
As usual the above is for home computers, if you are on a large network a lot of money can be lost from downtime.