Hi Stef,
I have the same camera - Sony DCR-TRV20E (the PAL version). As I purchased a new high definition Sony HDR-SR7 in February 2008, which records AVCHD to a hard drive, I hadn't used the DV tape camcorder with the newer versions of iMovie ('08, '09 and '11).
After seeing your original post today, I thought I should try importing some tape footage from the TRV20E. I'm very pleased to report that the import worked flawlessly! iMovie instantly recognised the camera and was able to control it - play, fast forward and rewind etc.
I appreciate that you may have followed Bengt's excellent advice, but just to reiterate, make sure that you follow these steps:
1. Launch iMovie and wait for it to be up and running;
2. Connect a FireWire 400 cable to the camera and to the Mac's FW port. Alternatively, you can connect the FW cable to an external FW hard drive that is connected to the Mac - I do this as my MacBook Pro has a FW 800 port only, while the hard drive has both FW 400 and 800. So, I use a 6 pin FW 400 cable with a mini connector on one end (for the camera) and a standard FW 400 connector on the other end. If you wish to connect directly to the Mac, and it has only a FW 800 port, you will need an adapter or a 9 pin to 6 pin cable, given that the camera uses FW 400. The Apple Store has this type of cable, but I'm not sure if it is available with the mini connector on the 6 pin end (FW 400);
3. Ensure that the camera is connected via mains power, not battery. Switch on the camera to the playback position. After a few seconds the camera should be recognised by iMovie and the Import screen should appear.
Note that I didn't have to set any Menu options in the camera, but upon checking after the import (approx. 20 minutes), I noticed that the item A/V⇒DV OUT was set to OFF - I think this is only set to ON when connecting composite cables from the camera to other devices (such as a TV). Composite cables use 3 RCA connectors - Yellow for video and Red and White for audio - with a mini plug on one end for input to the camera.
Hope this helps Stef. Rest assured that the Sony DCR-TRV20E does indeed work with iMovie '11. However, your setup may be different to mine (see my specs below), although you appear to be running Snow Leopard 10.6.5 as I am.
John