I just found out that Basha's Supermarket had some malware in its corporate system. The Mayor of Phoenix, my brother-in-law in Lake Havasu City, us, and many others were compromised by this malware. It also infected systems at Food City.
So, for us at least, we believe that Basha's is the culprit. The news bit said that when you swipe you card there, it was recorded and re-transmitted to someone who either sold the info or used it to create their own card.
I think that clears Quartzsite (at least for us). There was one day that we went to Lake Havasu City for some medical appointments and both the DW and I used our cards at Basha's. Their spokesperson said that the malware has been identified and removed; making the point-of-sale registers "safe" to use. Hmmm.