We verify all orders manually no matter how it's paid. This accomplishes two things for us. First it lets the client know we have received their order and allows us to reach out to the customer to understand their needs and see if what they ordered was actually a good fit for them or if they need something else even if it's not with us, and it allows us to verify information about the account.
Granted this takes extra time and we may loose some sales because we don't have "instant" activation, but I personally can sleep better at night knowing that we took some extra time to talk to our clients as well as prevented any possible fraud attempts.
In the event that something is unsettling with the call, we will ask the client to submit supporting documents verifying who they are and they are authorized for the transaction, especially for larger orders or unusual requests. Sometimes this may include a statement on company letter head, or the name/telephone number of the department manager, contacting the issuing bank of the card or check used for services to verify funds, and other methods.
The key to fraud prevention is to have many layers and trust your gut. When in doubt, verify.