I recently tried to make a small online from from a UK-based site. It was for 7 UK pounds. They declined the transaction. We called and they too were suspicious with the activity to a foreign country. Fair enough. But I had made identical 7 pound purchases from the same company earlier in the year. It can't be that difficult to check against previous transactions?
My other problem with our Visa-providing bank is that they allowed us to set up several alerts so we can be notified of suspicious activity. Unfortunately the first one occurred while I was driving in a foreign country. My wife called in while we drove, as we were both panicking that we would lose access to our card (and be unable to do mundane things like buy gasoline to reach our destination). Here the issue is my wife is the primary credit card holder. I am secondary only. The bank was annoyed that the alerts were set up to go to my email and cell phone rather than hers. I work with security stuff all of the time. My wife is somewhat technically illiterate. I need to see the alerts more than she does. They should let us decide who sees the alerts and recognize this situation too.