The ensuing negative publicity if ever a bank were to try and invoke that clause would be commercial suicide.
Make no mistake, banks try and encourage Internet Banking because it cuts their costs in terms of numbers of staff required. If they could get away with it, I'm sure they would close every branch excepting major cities.
To try and back out of their responsibility in all but the most blatant case is simply not an acceptable publicity risk.
There's nothing new in this. If you recall, having a Credit/Debit card with your PIN number written down close by, was also deemed unacceptable by the banks, and frankly, not unreasonably so.
As far as I can see, all they are saying is take reasonable care.
the nationwide has just sent us a card reader to use online but no instructions. went into local branch they knew nothing about them so not sure if the card reader is a scam or not anyone else got one.