This is an odd one. It is possible the prior owner had his dealer enable 'Passive Arming'. That arms the security system 30 secs after leaving the car and removing the key; it doesn't normally lock the doors though, just sets the security system to go off if a door is then opened.
The other possibility is an added aftermarket system that locks the doors. Over the years auction cars have come through with such devices. That seems to be a big thing in South Florida and Miami. Lots of cars from that area have had to have things like that removed when they get here to the Midwest. I know one fellow told me having such a device on his car was the only way he could get insurance while he lived there. Tells a tale of sorts, doesn't it??
Cheers,