Photoshop CS6 reads BIGTIFF, and is tested against the BIGTIFF samples from available libraries and applications. But we were unable to complete testing of writing BIGTIFF because there were not yet enough implementations to test against (my QE is kinda picky).
Although Adobe "officially" owns the TIFF specification, I believe that the support and evolution the TIFF format has primarily been handled through the open source LibTiff project.
That would be incorrect. Adobe still owns the TIFF standard, and works with other parties looking to extend TIFF. I have been working with the libtiff people for many years to make BIGTIFF happen. We have not yet had a chance to update the official TIFF documentation to include the BIGTIFF effort. (I keep asking for a tech writer to help with this huge document, and keep not getting one) Chris