Happened to my hubby too last week (seems someone bought bus tickets to an airport in Sweden via an on-line site!), although he did get a call from his bank before the Rendo e-mail.  Again, this happened just after a purchase he made on here, so there is something somewhere going on between events there.

Personally I never use my actual card online, but what my bank provides that they call e-card -- you specify allowed amount and a valid-until date -- but foremost PayPal.  Never had an issue with them, so can't say much about support or lack thereof, but I've had them for over 10 years now.