11.2.0.3: Gather stats job hangs due to parallel processing

While I did not actually post describing our issue (this post actually mentions the problem though) when we upgraded our DB to 11.2.0.3 on Exadata we ran into some serious issues as soon as we fired up all of our Gather Schema Statistics reports because of the parallelism that was enabled for the process.  Enter MOS note "Dbms_Stats.Gather_Table_Stats For a Table is Hanging With the Wait Event "PX Deq: Execute Reply"" via document ID 1946632.1 which sounds exactly the type of situation we had with our nodes conflicting with each other due to the parallel processing that was enabled!  Did we patch to fix the issue?  Nope, what we did was actually use the report parameter that gave us control over how many parallel processes would get spawned and then ran everything in a single Gather Schema Statistics report since we were on Exadata and had processing power to spare!