Who is he processing through? This sounds completely false as a person who has installed many of these things for people.
I've certainly seen some rough processor agreements, but most I've seen treat any form of payment on a particular card network the same (there are some processors where different card types cost more, but not necessarily how you use them). If that were the case, they can and should charge more for using the magstripe as a penalty and increased risk of fraud. ;-)
There's also the processors that are flat-rate and accept anything, which is great for small businesses - I had to have a long conversation with a group we set up with a Square installation (iPad, reader, etc.) that it didn't matter what kind of card it was since that "had heard stories that Amex costs more"