I see that no one ever replied. Since I love the Mac Rumors community, let's make sure we close this out.
I had a similar situation: time machine backup was via the network through my airport extreme. I disconnected the drive from the APE and connected to the new mac via USB (for faster speed). It showed up in finder, but not in Migration Assistant.
What worked for me was to mount the parsebundle so the computer can actually see the disk it needs to read off of. Basically double click the file saved inside the Backup Disk from the finder, and then it will show up as another disk. Once the parsebundle is mounted, it will show up as a "Time Machine Backups" disk or something similar. Try migration assistant again, you should be able to see the new disk, but it will have the name of your old computer. Proceed as normal from here.
Hope this helps.