Rapport for Online Banking actually does claim that it "Prevents malware infection, removes existing malware," in addition to other things, such as attempting to prevent many kinds of phishing attacks. However, I have never heard of it before now, so I don't know how well it does this job. Anti-virus software on a Mac is really not necessary at this time (see my Mac Malware Guide). The "man-in-the-browser" attacks that Rapport protects against rely on malware that does not currently exist for the Mac. The "man-in-the-middle" attacks can depend on malware or can be caused by hacking of network resources. It's far more likely for small ISP's domain name servers to be hacked, so you can avoid most of those attacks by using a DNS server like OpenDNS.
In all, I would tend to agree with peiper1. It sounds like your bank is using fairly draconian measures to ensure that they are not responsible for any fraud that might result from your use of their online banking. I would be quite nervous about using a bank that had that attitude. I would recommend that you seek out a bank that will protect you against online fraud, rather than trying to weasel out of their responsibility.