I decided to go ahead and get the 2012 V6 LaCrosse and picked it up last Saturday after a lot of research to make sure it was flat towable.
There is a GM document #PIP4973A titled "Dingy Towing Quick Reference for 6SP Front Wheel Drive Automatic Transmission for 2011 and 2012 - (Nov 21, 2011)" which provides information on which vehicles with which transmissions are and are not dingy towable. This document supersedes document #PIP4973. Your dealer should be able to get this document.
It basically states that the 2011 and 2012 Buick LaCrosse and Enclave, Cadillac SRX, Chevrolet Equinox, Impala, Malibu, and Traverse, and GMC Acadia and Terrain are all dingy towable providing they have the 6T70/75 (RPOs MH2, MH4, MH6, MY9) transmission. 2011 and 2012 Chevrolet Equinox and Malibu, GMC Terrain, and 2012 Chevrolet Sonic are also dingy towable providing they have the 6T30/6T40/6T45 (RPOs MHC, MH7, MH8, MH9) transmission.
The 2011-2012 Buick LaCrosse and Regal, Chevrolet Cruze, and 2012 Buick Verano, and Chevrolet Orlando (Canada only) are NOT dingy towable with the 6T30/6T40/6T45 (RPOs MHC, MHH, MH7, MH8, MH9) transmissions.
Notice that you cannot just go by the transmission. Sometimes a given transmissions is dingy towable and sometime not depending on which car it is used in.