When I was in college I could not afford a parking lot near campus so it was a hike to my truck. One hot Tucson day I hiked to the spot I parked my truck (1980 Toyota) unlocked the door, started it up and pulled out. Then I noticed the radio station was not what I listened to. Noticed women's clothing and make up in a bag on the floor. It was NOT my truck. I drove back to the lot. Put the truck back in the spot and went looking for my truck. I found it several rows back. Someone had apparently done the same thing i did because there was lipstick on the floor. I don't wear any. I drove to the front of the lot and there was a woman getting into the same year, make, model and color of my truck. Boy, did we have a good laugh over it because we both copped to driving away in the other person's truck. Then she decided to switch parking places because of the shade I had parked in. I probably would have done the same. She was hot too, but married. Oh well Fate laughing at me.
So the old lady's story is not all that implausible.