New iMac Can't Read Old Time Machine Disk

New 27 inch Retina iMac with 1T ssd and latest Yosemite. Have a Time Machine backup disk of my old iMac and I want to cherry pick some files off the old Time Machine Disk for use on the new machine. Absolutely can't figure out how to get the new iMac to read the old Time Machine disk and restore the selected files?

The Time Machine disk works fine on the old iMac and I can see all the backups and files. I can hook the time machine disk up to the new Retina iMac, start the Time Machine app (it's running with a new and different Time Machine hard drive). Then Shift+Cmd+c and see the old Time Machine disk. I can browse and see the actual Time Machine backup file structure but I can never get to anything that will highlight the restore button and let me work from that disk.

I don't want to start the new iMac Time Machine app with the old Time Machine disk for fear of loosing the old data.

Both iMacs are running the same latest Yosemite.

Before anyone answers, I know that I can just transfer from my old iMac data to a separate external hard drive, and then hook that hard drive to the new iMac and move them in. But I am doing thousands of photos and that takes twice as long. Besides, what good is a backup up that cant be accessed on a new machine. It destroys my confidence in Time Machine completely.

If my old iMac had crashed how could I recover any of the data to the new iMac???