Danish train confusion

So, on the train to Soro, after being evicted from my first seat, I found a seat in the next car, in first class -- as was obvious by the much more spatious seats. The first vacant seat was an aisle seat and there was a nice, older woman in the window seat.

I asked her if the seat next to her was vacant and she said yes. I stowed my heavy bag and sat down next to her. Many weeks of time has obscured who started the conversation, but we started talking. She was a Dane expatriate who lived in Switzerland. She was here on vacation going east to meet her husband, who was going to meet her in Jylland (Jutland).

She was a librarian and spoke English very well, but at some point it came up that I spoke some German, so she patiently conversed in German with me for a while. Then we switched back to English. She was roughly 60 and had grown up in Denmark but who had moved with her husband all over Europe and now lived in Switzerland. She had just come back from visiting her Mom, who, after a lifetime of good health, had suffered a serious injury and might eventually die from it.

She mentioned that she had a first-class seat reservation. I tried to ask her more about how Danish trains were setup due to my first seat-choice fiasco, but she admitted it had been many years since she had been back to her homeland.

We chatted off and on for most of the hour's ride to Soro. About 45 minutes in, the conductor finally came up to us. I presented my (2nd-class) ScanRail pass to him, waiting him to explain that I needed to pay more for taking up a first-class seat. He started talking in Danish to the woman next to me. Then he handed me my pass back.

I asked him if I was in first class and he said no, that I was fine. It turned out that the woman had picked the wrong car and was in a 2nd-class instead of her reserved 1st-class seat. Trying to avoid my earlier problem, I asked the conductor if there was any way of knowing whether a seat was reserved; he said that even he had no way of knowing! All he could do was ask for a person's ticket and see if the seat matched where the person was sitting.

The woman and I were amused that train travel was so complicated...even to Danes.