Internet Over the Phone Line?

On my last business trip I chose a place to stay because it was the only one with high speed Internet access in the room. I unpacked my computer and looked at the instructions:

1. Connect an RJ45 cable to your computer.
   
2. Turn on your computer. It's that simple.
   

There was a diagram showing a computer and a cable. There was an RJ45 cable on the table in my room. I attached it to my laptop, and stuck the other end in an appropriate socket in the telephone.

Nothing happened.

I looked dubiously at the phone. It had one thin wire coming out of it into the wall. For both voice and LAN? I called the desk and explained I didn't think my connection was working. I was told a technician would come to my room right away (at 9:30 PM!). Sure enough, a guy arrived in two minutes. He examined the situation carefully and took out another RJ45 cable, which he used to connect the telephone to the LAN outlet in the wall.

Duh. Why didn't I notice the LAN socket in the wall? I could have connected my computer directly to THAT.