I have an interesting story about dogs and memory.
When I was a kid we had toy poodles. My mom had one that was "hers" and I had one that was "mine". We would leave them in the laundry room when we weren't home. Our laundry room door sucked though and if you didn't close it right, the dogs could open the door. If there was any food on the table, the dogs would get to it before we got home. My mom and I would argue about who's dog was the "instigator" haha. So we had an idea... we set up a video camera!! We set up the video camera and intentionally didn't close the laundry room door correctly.
[side note: it is impossible for my family to leave without forgetting something, we often run back in the house after we've "left"]. So, we set up the camera and the whole family left (5 of us). We started the car, closed the doors, started to pull out, then went through the motions of "forgetting something". When my mom ran back in the house, the dogs still hadn't let themselves out of the laundry room. My mom came back to the car and we drove down the street. Then we PUSHED the car back so that the dogs couldn't hear the motor of the car approaching, lol. (We were kids so this was a lot of fun for us). Then we spied on the dogs through the windows to see who was being bad. Oh! and we had conveniently left some bread and milk on the table. After about 15-20 minutes of this fun, we walked into the house. The dogs were all excited like they normally were and acted like there was nothing wrong with them not being out of the laundry room. THEN we turned on the video! As soon as the dogs saw themselves on TV they FREAKED OUT!! They knew they were in trouble and they REMEMBERED doing it!! It was one of the funniest things I've ever seen. Interesting part of the video was that the dogs didn't let themselves out of the laundry room until you could hear that our car was gone. They REMEMBERED that we often would run back in because we forgot something and didn't want us to notice they were out and put them back in and properly close the door. Oh, and my mom's dog was the first one to get on the table
In conclusion, your friend is wrong. Dogs have great memories.