There are usually 6 crew members, and 2 Soyuz spacecraft on station. Each Soyuz carries 3 astronauts.
If there is an issue redocking during the move procedure, the backup plan is to return to earth. If they cannot redock and someone is left on the station, they would be stranded and cause all sorts of downstream issues.
So no, you do not need 3 to move a Soyuz, but because it is the ride home for 3 they need to be in it, in case they need to use it. For safety during launch and landing, each astronaut has a custom made seat liner, and they usually leave it in the Soyuz they intend to use.
This will get more interesting when they start using the commercial vendors, which are designed for 7 passengers (CST-100, DragonRider, Dream Chaser) but NASA is only planning on launching with 4 passengers (For a crew size of 7).